tests/rtest_integrate.mac

   1 /* A collection of about 730 integrals with power functions.
   2    The integrals are taken from functions.wolfram.com
   3
   4    OK   - The integral is solved by Maxima
   5    NEW  - Solution after extension of the integrator (rev. 1.34)
   6    NOUN - No solution a noun form is returned.
   7 */
   8
   9 (kill(all),
  10   declare(z,complex,n,integer),
  11   assume(n>0),
  12   assume(notequal(v,0)),
  13   domain:complex,
  14   radexpand:true,
  15
  16   /* This function checks if we get back the integrand.
  17    *
  18    * integral is the result of an integration,
  19    * var the integration variable, and
  20    * simplifier a simplifying function.
  21    */
  22   diffcheck(integral,var,simplifier):=
  23      if op(integral)=nounify(integrate) then
  24         integral
  25      else
  26         simplifier(diff(integral,var)),
  27
  28   factor_radcan(expr):=factor(radcan(expr)),
  29   done);
  30 done;
  31
  32 /* ----- Involving only one direct function --------------------------------- */
  33
  34 /* Problem 2: OK */
  35 integrate(a^(c*z),z);
  36 a^(c*z)/(log(a)*c);
  37
  38 /* Problem 3: OK */
  39 integrate(a^z,z);
  40 a^z/log(a);
  41
  42 /* Problem 4: OK */
  43 integrate(%e^(a*z+b),z);
  44 %e^(a*z+b)/a;
  45
  46 /* Problem 5: OK */
  47 integrate(%e^(a*z),z);
  48 %e^(a*z)/a;
  49
  50 /* Problem 6: OK */
  51 integrate(%e^z,z);
  52 %e^z;
  53
  54 /* ----- Power arguments and base a ----------------------------------------- */
  55
  56 /* Problem 7: NEW Type 1 */
  57 integrate(a^(b*z^r),z);
  58 z*gamma_incomplete(1/r,-b*z^r*log(a))*(-b*z^r*log(a))^(-1/r)/-r;
  59
  60 /* Problem 9: OK */
  61 assume(a>1,b>0);
  62 [a>1,b>0];
  63 integrate(a^(b*z^2),z),erf_representation:erfi,trigsign:true;
  64 -sqrt(%pi)*%i*erfi(%i*sqrt(-log(a)*b)*z)/(2*sqrt(-log(a)*b))$
  65 forget(a>1,b>0);
  66 [a>1,b>0];
  67
  68 /* Problem 11: OK */
  69 integrate(a^(b*sqrt(z)),z),radcan,factor;
  70 2*(log(a)*b*sqrt(z)-1)*a^(b*sqrt(z))/(log(a)^2*b^2);
  71
  72 /* Problem 12: NEW Type 1 */
  73 integrate(a^(b*(z^r)^p),z);
  74 z*gamma_incomplete(1/(p*r),-log(a)*b*(z^r)^p)
  75   /(-p*r*(-b*log(a)*(z^r)^p)^(1/(p*r)));
  76
  77 /* Problem 13: Expected failure
  78  * (z^r)^(1/r) simplifies to z which is not correct in general.
  79  * rischint does not respect the complex character of z.
  80  * The result of rischint is only correct for z>0.
  81  */
  82 integrate(a^(b*(z^r)^(1/r)),z), domain:real, radcan;
  83 a^(b*z)/(log(a)*b)$
  84
  85 /* Problem 14: Expected failure
  86  * sqrt(z^2) simplifies to z, which is not correct in general.
  87  * rischint does not respect the complex character of z.
  88  * The result of rischint is only correct for z>0.
  89  */
  90 integrate(a^(b*sqrt(z^2)),z), radcan;
  91 a^(b*z)/(log(a)*b)$
  92
  93 /* ----- Power arguments and base %e ---------------------------------------- */
  94
  95 /* Problem 15: NEW Type 1 */
  96 integrate(%e^(a*z^r),z);
  97 -z*gamma_incomplete(1/r,-a*z^r)/(r*(-a*z^r)^(1/r));
  98
  99 /* Problem 17: OK */
 100 assume(a>0);
 101 [a>0];
 102 integrate(%e^(a*z^2),z),erf_representation:erfi;
 103 -sqrt(%pi)*%i*erfi(%i*sqrt(-a)*z)/(2*sqrt(-a))$
 104 forget(a>0);
 105 [a>0];
 106
 107 /* Problem 19: OK */
 108 integrate(%e^(a*sqrt(z)),z);
 109 2*(a*sqrt(z)-1)*%e^(a*sqrt(z))/a^2;
 110
 111 /* Problem 20: NEW Type 1 */
 112 integrate(%e^(a*(z^r)^p),z);
 113 -z*gamma_incomplete(1/(p*r),-a*(z^r)^p)/(p*r*(-a*(z^r)^p)^(1/(p*r)));
 114
 115 /* Problem 21: Expected failure
 116  * See problem 13
 117  */
 118 integrate(%e^(a*(z^r)^(1/r)),z), domain:real;
 119 %e^(a*z)/a$
 120
 121 /* Problem 22: Expected failure
 122  * See problem 14
 123  */
 124 integrate(%e^(a*sqrt(z^2)),z);
 125 %e^(a*z)/a$
 126
 127 /* ----- Involving z^(v-1), arguments b*z and base a ------------------------ */
 128
 129 /* Problem 23: NEW Type 2 */
 130 integrate(z^(v-1)*a^(b*z),z);
 131 -z^v*gamma_incomplete(v,-log(a)*b*z)/(-b*z*log(a))^v;
 132
 133 /* Problem 24: NEW Type 2 */
 134 integrate(a^(b*z)/z,z),gamma_expand:true,logcontract;
 135 expintegral_ei(b*z*log(a));
 136
 137 /* Problem 25: NEW Type 2 */
 138 integrate(z^(v-1)*a^z,z);
 139 -gamma_incomplete(v,-log(a)*z)*z^v/(-log(a)*z)^v;
 140
 141 /* Problem 26: NEW Type 2 */
 142 integrate(a^z/z,z),gamma_expand:true,logcontract;
 143 expintegral_ei(z*log(a));
 144
 145
 146 /* ----- Involving z^(v-1), arguments a*z and base %e ----------------------- */
 147
 148 /* Problem 27: NEW Type 2 */
 149 integrate(z^(v-1)*%e^(a*z),z);
 150 -gamma_incomplete(v,-a*z)*z^v/(-a*z)^v;
 151
 152 /* Problem 28: NEW Type 2 */
 153 integrate(z^(v-1)*%e^z,z);
 154 -gamma_incomplete(v,-z)*z^v/(-z)^v;
 155
 156 /* Problem 29: NEW Type 2 */
 157 integrate(z^n*%e^(a*z),z),factor;
 158 a^(-n-1)*(-1)^n*gamma_incomplete(n+1,-a*z);
 159
 160 /* Problem 30: New Type 2 */
 161 integrate(%e^(a*z)/z^n,z),factor;
 162 a^(n-1)*(-1)^n*gamma_incomplete(1-n,-a*z);
 163
 164 /* Problem 31: OK */
 165 integrate(z*%e^(a*z),z);
 166 (a*z-1)*%e^(a*z)/a^2;
 167
 168 /* Problem 32: Expected failure
 169  * Simplifies sqrt(z^2) -> z, which is correct only for z>0.
 170  * The problem is in rischint.
 171  */
 172 integrate(sqrt(z^2)*%e^(a*z),z);
 173 (a*z-1)*%e^(a*z)/a^2$
 174
 175 /* Problem 33: OK */
 176 integrate(z^2*%e^(a*z),z);
 177 (a^2*z^2-2*a*z+2)*%e^(a*z)/a^3;
 178
 179 /* Problem 34: OK */
 180 integrate(z^3*%e^(a*z),z);
 181 (a^3*z^3-3*a^2*z^2+6*a*z-6)*%e^(a*z)/a^4;
 182
 183 /* Problem 35: OK */
 184 integrate(z^4*%e^(a*z),z);
 185 (a^4*z^4-4*a^3*z^3+12*a^2*z^2-24*a*z+24)*%e^(a*z)/a^5;
 186
 187 /* Problem 36: OK */
 188 integrate(z^5*%e^(a*z),z);
 189 (a^5*z^5-5*a^4*z^4+20*a^3*z^3-60*a^2*z^2+120*a*z-120)*%e^(a*z)/a^6;
 190
 191 /* Problem 37: OK */
 192 integrate(z^6*%e^(a*z),z);
 193 (a^6*z^6-6*a^5*z^5+30*a^4*z^4-120*a^3*z^3+360*a^2*z^2-720*a*z+720)
 194         *%e^(a*z)
 195         /a^7;
 196
 197 /* Problem 38: OK */
 198 integrate(z^7*%e^(a*z),z);
 199 (a^7*z^7-7*a^6*z^6+42*a^5*z^5-210*a^4*z^4+840*a^3*z^3-2520*a^2*z^2
 200                +5040*a*z-5040)
 201         *%e^(a*z)
 202         /a^8;
 203
 204 /* Problem 39: OK */
 205 integrate(z^8*%e^(a*z),z);
 206 (a^8*z^8-8*a^7*z^7+56*a^6*z^6-336*a^5*z^5+1680*a^4*z^4-6720*a^3*z^3
 207                +20160*a^2*z^2-40320*a*z+40320)
 208         *%e^(a*z)
 209         /a^9;
 210
 211 /* Problem 40: NEW Type 2 */
 212 integrate(%e^(a*z)/z,z),gamma_expand:true,logcontract;
 213 expintegral_ei(a*z);
 214
 215 /* Problem 41: NEW Type 2 */
 216 integrate(%e^(a*z)/z^2,z),gamma_expand:true,logcontract,ratsimp;
 217 (a*z*expintegral_ei(a*z)-%e^(a*z))/z;
 218
 219 /* Problem 42: NEW Type 2 */
 220 integrate(%e^(a*z)/z^3,z),gamma_expand:true,logcontract,ratsimp;
 221 (a^2*z^2*expintegral_ei(a*z)+(-a*z-1)*%e^(a*z))/(2*z^2);
 222
 223 /* Problem 43: NEW Type 2 */
 224 integrate(%e^(a*z)/z^4,z),gamma_expand:true,logcontract,ratsimp;
 225 (a^3*z^3*expintegral_ei(a*z)+(-a^2*z^2-a*z-2)*%e^(a*z))/(6*z^3);
 226
 227 /* Problem 44: NEW Type 2 */
 228 integrate(%e^(a*z)/z^5,z),gamma_expand:true,logcontract,ratsimp;
 229 (a^4*z^4*expintegral_ei(a*z)+(-a^3*z^3-a^2*z^2-2*a*z-6)*%e^(a*z))/(24*z^4);
 230
 231 /* Problem 45: NEW Type 2 (OK)
 232  * The following gives sqrt(z)/sqrt(-z) and not sqrt(-z)/sqrt(z),
 233  * but the phase is correct.
 234  */
 235 integrate(z^(1/2+n)*%e^(a*z),z),ratsimp;
 236 a^(-n-1)*(-1)^n*gamma_incomplete((2*n+3)/2,-a*z)*sqrt(z)/sqrt(-a*z);
 237
 238 /* Problem 47: OK */
 239 assume(a>0);
 240 [a>0];
 241 integrate(sqrt(z)*%e^(a*z),z),erf_representation:erfi,expand;
 242 sqrt(z)*%e^(a*z)/a+sqrt(%pi)*%i*erfi(%i*sqrt(-a)*sqrt(z))/(2*sqrt(-a)*a)$
 243 forget(a>0);
 244 [a>0];
 245
 246 /* Problem 50: OK */
 247 assume(a>0);
 248 [a>0];
 249 multthru(integrate(z^(3/2)*%e^(a*z),z)),erf_representation:erfi;
 250 (2*a*z^(3/2)-3*sqrt(z))*%e^(a*z)/(2*a^2)
 251  -3*sqrt(%pi)*%i*erfi(%i*sqrt(-a)*sqrt(z))/(4*sqrt(-a)*a^2)$
 252 forget(a>0);
 253 [a>0];
 254
 255 /* Problem 53: OK */
 256 assume(a>0);
 257 [a>0];
 258 multthru(integrate(z^(5/2)*%e^(a*z),z)),erf_representation:erfi;
 259 (4*a^2*z^(5/2)-10*a*z^(3/2)+15*sqrt(z))*%e^(a*z)/(4*a^3)
 260  +15*sqrt(%pi)*%i*erfi(%i*sqrt(-a)*sqrt(z))/(8*sqrt(-a)*a^3);
 261 forget(a>0);
 262 [a>0];
 263
 264 /* Problem 56: OK */
 265 assume(a>0);
 266 [a>0];
 267 multthru(integrate(z^(7/2)*%e^(a*z),z)),erf_representation:erfi;
 268 (8*a^3*z^(7/2)-28*a^2*z^(5/2)+70*a*z^(3/2)-105*sqrt(z))*%e^(a*z)/(8*a^4)
 269  -105*sqrt(%pi)*%i*erfi(%i*sqrt(-a)*sqrt(z))/(16*sqrt(-a)*a^4);
 270 forget(a>0);
 271 [a>0];
 272
 273 /* Problem 59: OK */
 274 assume(a>0);
 275 [a>0];
 276 multthru(integrate(z^(9/2)*%e^(a*z),z)),erf_representation:erfi;
 277 (16*a^4*z^(9/2)-72*a^3*z^(7/2)+252*a^2*z^(5/2)-630*a*z^(3/2)+945*sqrt(z))
 278  *%e^(a*z)
 279  /(16*a^5)
 280  +945*sqrt(%pi)*%i*erfi(%i*sqrt(-a)*sqrt(z))/(32*sqrt(-a)*a^5)$
 281 forget(a>0);
 282 [a>0];
 283
 284 /* Problem 62: OK */
 285 assume(a>0);
 286 [a>0];
 287 integrate(%e^(a*z)/sqrt(z),z),erf_representation:erfi;
 288 -sqrt(%pi)*%i*erfi(%i*sqrt(-a)*sqrt(z))/sqrt(-a)$
 289 forget(a>0);
 290 [a>0];
 291
 292 /* Problem 64: NEW Type 2 (OK)
 293  * We have a problem to simplify this integral to an erfi representation,
 294  * because of expression like sqrt(-z), which do not simplify to %i*sqrt(z).
 295  * We give the results in term of the erfc function.
 296  * The same for No. 48, 49, 50, 51
 297  */
 298 multthru(integrate(%e^(a*z)/z^(3/2),z)),gamma_expand:true;
 299 2*sqrt(%pi)*sqrt(-a*z)*erfc(sqrt(-a*z))/sqrt(z)-2*%e^(a*z)/sqrt(z);
 300
 301 /* Problem 65: NEW Type 2 (OK)
 302  * Maxima simplifies z/sqrt(z^3) -> 1/sqrt(z). Therefore, we get the same
 303  * result for Problem 64 and 65.
 304  * Because of revision 1.125 of simp.lisp Maxima no longer simplifies
 305  * z/sqrt(z^3) -> 1/sqrt(z). We get a noun form.
 306  */
 307 multthru(integrate(%e^(a*z)/sqrt(z^3),z)),gamma_expand:true, domain:real;
 308 2*sqrt(%pi)*sqrt(-a*z)*erfc(sqrt(-a*z))/sqrt(z)-2*%e^(a*z)/sqrt(z)$
 309 /*'integrate(%e^(a*z)/sqrt(z^3),z);*/
 310
 311 /* Problem 66: NEW Type 2 (OK) */
 312 multthru(integrate(%e^(a*z)/z^(5/2),z)),gamma_expand:true;
 313 (-4*a*z/3-2/3)*%e^(a*z)/z^(3/2)-4*sqrt(%pi)*(-a*z)^(3/2)*erfc(sqrt(-a*z))
 314                                 /(3*z^(3/2));
 315
 316 /* Problem 67: NEW Type 2 (OK) */
 317 multthru(integrate(%e^(a*z)/z^(7/2),z)),gamma_expand:true;
 318 8*sqrt(%pi)*(-a*z)^(5/2)*erfc(sqrt(-a*z))/(15*z^(5/2))
 319  +(-8*a^2*z^2/15-4*a*z/15-2/5)*%e^(a*z)/z^(5/2);
 320
 321 /* Problem 68: NEW Type 2 (OK) */
 322 multthru(integrate(%e^(a*z)/z^(9/2),z)),gamma_expand:true;
 323 (-16*a^3*z^3/105-8*a^2*z^2/105-4*a*z/35-2/7)*%e^(a*z)/z^(7/2)
 324  -16*sqrt(%pi)*(-a*z)^(7/2)*erfc(sqrt(-a*z))/(105*z^(7/2));
 325
 326 /* ----- Involving z^(v-1), arguments b*z+d and base a ---------------------- */
 327
 328 /* Problem 69: NEW Type 2 */
 329 integrate(z^(v-1)*a^(b*z+d),z);
 330 -a^d*gamma_incomplete(v,-log(a)*b*z)*z^v/(-log(a)*b*z)^v$
 331
 332 /* Problem 70: NEW 2 */
 333 integrate(a^(b*z+d)/z,z),gamma_expand:true,logcontract;
 334 a^d*expintegral_ei(b*z*log(a));
 335
 336 /* ----- Involving z^(v-1), arguments b*z+d and base %e --------------------- */
 337
 338 /* Problem 71: NEW 2 */
 339 diffcheck(integrate(z^(v-1)*%e^(a*z+b),z),z,factor);
 340 z^(v-1)*%e^(a*z+b);
 341
 342 /* Problem 72: NEW 2 */
 343 integrate(z^n*%e^(a*z+b),z),factor;
 344 a^(-n-1)*%e^b*(-1)^n*gamma_incomplete(n+1,-a*z);
 345
 346 /* Problem 73: OK */
 347 integrate(z*%e^(a*z+b),z),factor;
 348 (a*z-1)*%e^(a*z+b)/a^2;
 349
 350 /* Problem 74: NEW 2 */
 351 integrate(%e^(a*z+b)/z,z),gamma_expand:true,logcontract;
 352 %e^b*expintegral_ei(a*z);
 353
 354 /* Problem 76: OK */
 355 assume(a>0);
 356 [a>0];
 357 integrate(%e^(a*z+b)/sqrt(z),z),erf_representation:erfi;
 358 -sqrt(%pi)*%i*%e^b*erfi(%i*sqrt(-a)*sqrt(z))/sqrt(-a)$
 359 forget(a>0);
 360 [a>0];
 361
 362 /* ----- Involving z^(v-1), arguments b*z^r and base a ---------------------- */
 363
 364 /* Problem 77: NEW 2 */
 365 integrate(z^(v-1)*a^(b*z^r),z);
 366 -gamma_incomplete(v/r,-log(a)*b*z^r)*z^v/(r*(-log(a)*b*z^r)^(v/r))$
 367
 368 /* Problem 79: NEW 2 */
 369 integrate(a^(b*z^r)/z,z),gamma_expand:true,logcontract;
 370 expintegral_ei(log(a)*b*z^r)/r;
 371
 372 /* ----- Involving z^(v-1), arguments a*z^r and base %e --------------------- */
 373
 374 /* Problem 80: NEW 2 */
 375 integrate(z^(v-1)*%e^(a*z^r),z);
 376 -gamma_incomplete(v/r,-a*z^r)*z^v/(r*(-a*z^r)^(v/r))$
 377
 378 /* Problem 81: NEW 2 */
 379 integrate(%e^(a*z^r)/z,z),gamma_expand:true,logcontract;
 380 expintegral_ei(a*z^r)/r;
 381
 382 /* Problem 82: NEW 2 */
 383 integrate(z^(2*n)*%e^(a*z^2),z),factor;
 384 -(-1)^n*gamma_incomplete((2*n+1)/2,-a*z^2)*z/(2*a^n*sqrt(-a*z^2))$
 385
 386 /* Problem 83: NEW 2 */
 387 integrate(z^(2*n-1)*%e^(a*z^2),z),factor;
 388 -(-1)^n*gamma_incomplete(n,-a*z^2)/(2*a^n);
 389
 390 /* Problem 84: OK */
 391 integrate(z*%e^(a*z^2),z);
 392 %e^(a*z^2)/(2*a);
 393
 394 /* Problem 86: OK */
 395 assume(a>0);
 396 [a>0];
 397 integrate(z^2*%e^(a*z^2),z),erf_representation:erfi;
 398 sqrt(%pi)*%i*erfi(%i*sqrt(-a)*z)/(4*sqrt(-a)*a)+z*%e^(a*z^2)/(2*a)$
 399 forget(a>0);
 400 [a>0];
 401
 402 /* Problem 88: OK */
 403 integrate(z^3*%e^(a*z^2),z);
 404 (a*z^2-1)*%e^(a*z^2)/(2*a^2);
 405
 406 /* Problem 90: OK */
 407 assume(a>0);
 408 [a>0];
 409 integrate(z^4*%e^(a*z^2),z),erf_representation:erfi;
 410 (2*a*z^3-3*z)*%e^(a*z^2)/(4*a^2)-3*sqrt(%pi)*%i*erfi(%i*sqrt(-a)*z)
 411                                  /(8*sqrt(-a)*a^2)$
 412 forget(a>0);
 413 [a>0];
 414
 415 /* Problem 92: OK */
 416 integrate(z^5*%e^(a*z^2),z);
 417 (a^2*z^4-2*a*z^2+2)*%e^(a*z^2)/(2*a^3);
 418
 419 /* Problem 93: NEW 2 */
 420 integrate(%e^(a*z^2)/z,z),gamma_expand:true,logcontract;
 421 expintegral_ei(a*z^2)/2;
 422
 423 /* Problem 94: NEW 2 */
 424 multthru(integrate(%e^(a*z^2)/z^2,z)), gamma_expand:true;
 425 sqrt(%pi)*sqrt(-a*z^2)*erfc(sqrt(-a*z^2))/z-%e^(a*z^2)/z;
 426
 427 /* Problem 95: NEW 2 */
 428 integrate(%e^(a*z^2)/z^3,z),gamma_expand:true,logcontract,ratsimp;
 429 (a*z^2*expintegral_ei(a*z^2)-%e^(a*z^2))/(2*z^2);
 430
 431 /* Problem 96: NEW 2 */
 432 integrate(%e^(a*z^2)/z^4,z), gamma_expand:true,ratsimp;
 433 (2*sqrt(%pi)*a^2*z^4*erfc(sqrt(-a*z^2))+sqrt(-a*z^2)*(2*a*z^2+1)*%e^(a*z^2))
 434  /(3*z^3*sqrt(-a*z^2))/-1;
 435
 436 /* Problem 97: NEW 2 */
 437 integrate(%e^(a*z^2)/z^5,z),gamma_expand:true,logcontract;
 438 (2*a^2*z^4*expintegral_ei(a*z^2)+(-2*a*z^2-2)*%e^(a*z^2))/(8*z^4);
 439
 440 /* Problem 98: NEW 2 */
 441 integrate(z^n*%e^(a*sqrt(z)),z);
 442 -2*gamma_incomplete(2*(n+1),-a*sqrt(z))/a^(2*(n+1));
 443
 444 /* Problem 99: OK */
 445 integrate(z*%e^(a*sqrt(z)),z);
 446 2*(a^3*z^(3/2)-3*a^2*z+6*a*sqrt(z)-6)*%e^(a*sqrt(z))/a^4;
 447
 448 /* Problem 100: OK */
 449 integrate(z^2*%e^(a*sqrt(z)),z);
 450 2*(a^5*z^(5/2)-5*a^4*z^2+20*a^3*z^(3/2)-60*a^2*z+120*a*sqrt(z)-120)
 451         *%e^(a*sqrt(z))
 452         /a^6;
 453
 454 /* Problem 101: OK */
 455 integrate(z^3*%e^(a*sqrt(z)),z);
 456 2*(a^7*z^(7/2)-7*a^6*z^3+42*a^5*z^(5/2)-210*a^4*z^2+840*a^3*z^(3/2)
 457                      -2520*a^2*z+5040*a*sqrt(z)-5040)*%e^(a*sqrt(z))
 458         /a^8;
 459
 460 /* Problem 102: OK */
 461 integrate(z^4*%e^(a*sqrt(z)),z);
 462 2*(a^9*z^(9/2)-9*a^8*z^4+72*a^7*z^(7/2)-504*a^6*z^3+3024*a^5*z^(5/2)
 463                      -15120*a^4*z^2+60480*a^3*z^(3/2)-181440*a^2*z
 464                      +362880*a*sqrt(z)-362880)*%e^(a*sqrt(z))
 465         /a^10;
 466
 467 /* Problem 103: OK */
 468 integrate(z^5*%e^(a*sqrt(z)),z);
 469 2*(a^11*z^(11/2)-11*a^10*z^5+110*a^9*z^(9/2)-990*a^8*z^4
 470                        +7920*a^7*z^(7/2)-55440*a^6*z^3+332640*a^5*z^(5/2)
 471                        -1663200*a^4*z^2+6652800*a^3*z^(3/2)-19958400*a^2*z
 472                        +39916800*a*sqrt(z)-39916800)*%e^(a*sqrt(z))
 473         /a^12;
 474
 475 /* Problem 104: NEW 2 */
 476 integrate(%e^(a*sqrt(z))/z,z),gamma_expand:true,logcontract;
 477 2*expintegral_ei(a*sqrt(z));
 478
 479 /* Problem 105: NEW 2 */
 480 integrate(%e^(a*sqrt(z))/z^2,z),gamma_expand:true,logcontract;
 481 ((2*a*z+2*sqrt(z))*%e^(a*sqrt(z))-2*a^2*expintegral_ei(a*sqrt(z))*z^(3/2))
 482  /-(2*z^(3/2));
 483
 484 /* Problem 106: NEW 2 */
 485 integrate(%e^(a*sqrt(z))/z^3,z),gamma_expand:true,logcontract;
 486 ((2*a^3*z^3+2*a^2*z^(5/2)+4*a*z^2+12*z^(3/2))*%e^(a*sqrt(z))
 487  -2*a^4*expintegral_ei(a*sqrt(z))*z^(7/2))
 488  /-(24*z^(7/2));
 489
 490 /* Problem 107: NEW 2 */
 491 integrate(%e^(a*sqrt(z))/z^4,z),gamma_expand:true,logcontract;
 492 ((2*a^5*z^5+2*a^4*z^(9/2)+4*a^3*z^4+12*a^2*z^(7/2)+48*a*z^3+240*z^(5/2))
 493  *%e^(a*sqrt(z))
 494  -2*a^6*expintegral_ei(a*sqrt(z))*z^(11/2))
 495  /-(720*z^(11/2));
 496
 497 /* Problem 108: NEW 2 */
 498 integrate(%e^(a*sqrt(z))/z^5,z),gamma_expand:true,logcontract;
 499 ((2*a^7*z^7+2*a^6*z^(13/2)+4*a^5*z^6+12*a^4*z^(11/2)+48*a^3*z^5
 500             +240*a^2*z^(9/2)+1440*a*z^4+10080*z^(7/2))
 501  *%e^(a*sqrt(z))
 502  -2*a^8*expintegral_ei(a*sqrt(z))*z^(15/2))
 503  /-(40320*z^(15/2));
 504
 505 /* ----- Involving z^(v-1), arguments b*z^r and base a ---------------------- */
 506
 507 /* Problem 109: NEW 2 */
 508 diffcheck(integrate(z^(v-1)*a^(d+b*z^r),z),z,radcan);
 509 z^(v-1)*a^(d+b*z^r);
 510
 511 /* Problem 110: NEW 2 */
 512 integrate(a^(d+b*z^r)/z,z),gamma_expand:true,logcontract;
 513 a^d*expintegral_ei(log(a)*b*z^r)/r;
 514
 515 /* ----- Involving z^(v-1), arguments b*z^r and base %e --------------------- */
 516
 517 /* Problem 111: NEW 2 */
 518 diffcheck(integrate(z^(v-1)*%e^(b+a*z^r),z),z,factor);
 519 z^(v-1)*%e^(b+a*z^r);
 520
 521 /* Problem 112: NEW 2 */
 522 integrate(%e^(b+a*z^r)/z,z),gamma_expand:true,logcontract;
 523 %e^b*expintegral_ei(a*z^r)/r;
 524
 525 /* ----- Involving (a*z+b)^-n ----------------------------------------------- */
 526
 527 /* Problem 113: NEW 3 */
 528 integrate(%e^(c*z)/(b+a*z),z),expintexpand:true,logcontract;
 529 %e^-(b*c/a)*expintegral_ei((a*c*z+b*c)/a)/a;
 530
 531 /* Problem 114: NEW 3 */
 532 integrate(%e^(c*z)/(b+a*z)^2,z);
 533 -expintegral_e(2,-c*(a*z+b)/a)*%e^-(b*c/a)/(a*(a*z+b));
 534
 535 /* Problem 115: NEW 3 */
 536 integrate(%e^(c*z)/(b+a*z)^3,z);
 537 -expintegral_e(3,-c*(a*z+b)/a)*%e^-(b*c/a)/(a*(a*z+b)^2);
 538
 539 /* Problem 116: NEW 3 */
 540 integrate(%e^(c*z)/(b+a*z)^4,z);
 541 -expintegral_e(4,-c*(a*z+b)/a)*%e^-(b*c/a)/(a*(a*z+b)^3);
 542
 543 /* Problem 117: NEW 3 */
 544 integrate(%e^(c*z)/(b+a*z)^5,z);
 545 -expintegral_e(5,-c*(a*z+b)/a)*%e^-(b*c/a)/(a*(a*z+b)^4);
 546
 547 /* Problem 118: NEW 3 */
 548 integrate(%e^(c*z)/(b+a*z)^6,z);
 549 -expintegral_e(6,-c*(a*z+b)/a)*%e^-(b*c/a)/(a*(a*z+b)^5);
 550
 551 /* Problem 119: NOUN
 552  * This integral and the integrals 120, 121, 122, 123, 124 return an
 553  * unevaluated integral. This is caused by rischint. Some of the integrals
 554  * can be integrated in a second step. The algorithm can be improved.
 555  */
 556 integrate(z*%e^(c*z)/(b+a*z),z);
 557 z*%e^(c*z)/(a*c*z+b*c)-b*'integrate(%e^(c*z)/(a^2*c*z^2+2*a*b*c*z+b^2*c),z);
 558
 559 /* Problem 120: NOUN */
 560 integrate(z^2*%e^(c*z)/(b+a*z),z);
 561 (c*z^2-z)*%e^(c*z)/(a*c^2*z+b*c^2)-'integrate(
 562                                    (b*c*z-b)*%e^(c*z)
 563                                     /(a^2*c^2*z^2+2*a*b*c^2*z+b^2*c^2),z);
 564
 565 /* Problem 121: NOUN */
 566 integrate(z*%e^(c*z)/(b+a*z)^2,z);
 567 'integrate((a*z-b)*%e^(c*z)/(a^3*c*z^3+3*a^2*b*c*z^2+3*a*b^2*c*z+b^3*c),z)
 568  +z*%e^(c*z)/(a^2*c*z^2+2*a*b*c*z+b^2*c);
 569
 570 /* Problem 122: NOUN */
 571 integrate(z^2*%e^(c*z)/(b+a*z)^2,z);
 572 z^2*%e^(c*z)/(a^2*c*z^2+2*a*b*c*z+b^2*c)
 573  -2*b*'integrate(z*%e^(c*z)/(a^3*c*z^3+3*a^2*b*c*z^2+3*a*b^2*c*z+b^3*c),z);
 574
 575 /* Problem 123: NOUN */
 576 integrate(z^3*%e^(c*z)/(b+a*z)^2,z);
 577 'integrate((2*b^2*c*z+2*b^2)*%e^(c*z)/(a^4*c^2*z^3+3*a^3*b*c^2*z^2
 578                                        +3*a^2*b^2*c^2*z+a*b^3*c^2),z)
 579   +(a*c*z^3-a*z^2-2*b*z)*%e^(c*z)/(a^3*c^2*z^2+2*a^2*b*c^2*z+a*b^2*c^2);
 580
 581 /* Problem 124: NOUN */
 582 integrate(z^4*%e^(c*z)/(b+a*z)^2,z);
 583 'integrate(((2*a*b^2*c-2*b^3*c^2)*z-2*b^3*c-4*a*b^2)*%e^(c*z)
 584             /(a^5*c^3*z^3+3*a^4*b*c^3*z^2+3*a^3*b^2*c^3*z+a^2*b^3*c^3),z)
 585  +(a^2*c^2*z^4-2*a^2*c*z^3+(2*a^2-2*a*b*c)*z^2+(2*b^2*c+4*a*b)*z)*%e^(c*z)
 586   /(a^4*c^3*z^2+2*a^3*b*c^3*z+a^2*b^2*c^3);
 587
 588 /* ----- Involving (a*z^2+b)^-n and base %e --------------------------------- */
 589
 590 /* Problem 125: NOUN */
 591 integrate(%e^(c*z)/(b+a*z^2),z);
 592 'integrate(%e^(c*z)/(a*z^2+b),z);
 593
 594 /* Problem 126: NOUN */
 595 integrate(z*%e^(c*z)/(b+a*z^2),z);
 596 'integrate((a*z^2-b)*%e^(c*z)/(a^2*c*z^4+2*a*b*c*z^2+b^2*c),z)
 597  +z*%e^(c*z)/(a*c*z^2+b*c);
 598
 599 /* Problem 127: NOUN */
 600 integrate(%e^(c*z)/(b+a*z^2)^2,z);
 601 'integrate(%e^(c*z)/(a*z^2+b)^2,z);
 602
 603 /* Problem 128: NOUN */
 604 integrate(z*%e^(c*z)/(b+a*z^2)^2,z);
 605 'integrate((3*a*z^2-b)*%e^(c*z)/(a^3*c*z^6+3*a^2*b*c*z^4+3*a*b^2*c*z^2+b^3*c),z)
 606  +z*%e^(c*z)/(a^2*c*z^4+2*a*b*c*z^2+b^2*c);
 607
 608 /* ----- Involving (a*z^2+b*z+c)^-n ----------------------------------------- */
 609
 610 /* Problem 129: NOUN */
 611 integrate(%e^(d*z)/(c+b*z+a*z^2),z);
 612 'integrate(%e^(d*z)/(a*z^2+b*z+c),z);
 613
 614 /* Problem 130: NOUN */
 615 integrate(z*%e^(d*z)/(c+b*z+a*z^2),z);
 616 'integrate((a*z^2-c)*%e^(d*z)/(a^2*d*z^4+2*a*b*d*z^3+(2*a*c*d+b^2*d)*z^2
 617                                         +2*b*c*d*z+c^2*d),z)
 618  +z*%e^(d*z)/(a*d*z^2+b*d*z+c*d);
 619
 620 /* Problem 131: NOUN */
 621 integrate(%e^(d*z)/(c+b*z+a*z^2)^2,z);
 622 'integrate(%e^(d*z)/(a*z^2+b*z+c)^2,z);
 623
 624 /* Problem 132: NOUN */
 625 integrate(z*%e^(d*z)/(c+b*z+a*z^2)^2,z);
 626 'integrate((3*a*z^2+b*z-c)*%e^(d*z)/(a^3*d*z^6+3*a^2*b*d*z^5
 627                                               +(3*a^2*c*d+3*a*b^2*d)*z^4
 628                                               +(6*a*b*c*d+b^3*d)*z^3
 629                                               +(3*a*c^2*d+3*b^2*c*d)*z^2
 630                                               +3*b*c^2*d*z+c^3*d),z)
 631  +z*%e^(d*z)/(a^2*d*z^4+2*a*b*d*z^3+(2*a*c*d+b^2*d)*z^2+2*b*c*d*z+c^2*d);
 632
 633 /* ----- Involving (a*z*b)^w and base %e ------------------------------------ */
 634
 635 /* Problem 133: NEW 3 */
 636 integrate((a*z+b)^w*%e^(c*z+d),z);
 637 -%e^(d-b*c/a)*expintegral_e(-w,-c*(a*z+b)/a)*(a*z+b)^(w+1)/a;
 638
 639 /* Problem 134: NEW 3 */
 640 integrate((a*z+b)^w*%e^(c*z),z);
 641 -%e^-(b*c/a)*expintegral_e(-w,-c*(a*z+b)/a)*(a*z+b)^(w+1)/a;
 642
 643 /* Problem 135: OK */
 644 multthru(integrate((a*z+b)^(3/2)*%e^(c*z),z));
 645 3*sqrt(%pi)*a*%e^-(b*c/a)*erf(sqrt(-c/a)*sqrt(a*z+b))/(4*c^2*sqrt(-c/a))
 646  +(2*a*c*(a*z+b)^(3/2)-3*a^2*sqrt(a*z+b))*%e^(c*(a*z+b)/a-b*c/a)/(2*a*c^2);
 647
 648 /* Problem 136: OK */
 649 multthru(integrate(sqrt(a*z+b)*%e^(c*z),z));
 650 sqrt(a*z+b)*%e^(c*(a*z+b)/a-b*c/a)/c-sqrt(%pi)*%e^-(b*c/a)
 651                                               *erf(sqrt(-c/a)*sqrt(a*z+b))
 652                                      /(2*c*sqrt(-c/a));
 653
 654 /* Problem 137: OK */
 655 integrate(%e^(c*z)/sqrt(a*z+b),z);
 656 sqrt(%pi)*%e^-(b*c/a)*erf(sqrt(-c/a)*sqrt(a*z+b))/(a*sqrt(-c/a));
 657
 658 /* Problem 138: NEW 2
 659  * This example is first transformed to an example of type 2.
 660  */
 661 diffcheck(integrate(%e^(c*z)/(a*z+b)^(3/2),z),z,factor);
 662 %e^(c*z)/(a*z+b)^(3/2);
 663
 664 /* ----- Involving a*z^2+b*z+c ---------------------------------------------- */
 665
 666 /* Problem 139: OK */
 667 integrate(d^(c+b*z+a*z^2),z),erf_representation:erfi,radexpand:all,factor;
 668 sqrt(%pi)*d^c*%e^-(b^2*log(d)/(4*a))*erfi(sqrt(log(d))*(2*a*z+b)/(2*sqrt(a)))
 669  /(2*sqrt(a)*sqrt(log(d)));
 670
 671 /* Problem 140: OK */
 672 integrate(%e^(c+b*z+a*z^2),z),erf_representation:erfi,radexpand:all,factor;
 673 sqrt(%pi)*%e^(c-b^2/(4*a))*erfi((2*a*z+b)/(2*sqrt(a)))/(2*sqrt(a));
 674
 675 /* ----- Involving a*z^2+b -------------------------------------------------- */
 676
 677 /* Problem 141: OK */
 678 integrate(d^(b*z+a*z^2),z),erf_representation:erfi,radexpand:all,factor;
 679 sqrt(%pi)*%e^-(b^2*log(d)/(4*a))*erfi(sqrt(log(d))*(2*a*z+b)/(2*sqrt(a)))
 680  /(2*sqrt(a)*sqrt(log(d)));
 681
 682 /* Problem 142: OK */
 683 integrate(%e^(b*z+a*z^2),z),erf_representation:erfi,radexpand:all,factor;
 684 sqrt(%pi)*%e^-(b^2/(4*a))*erfi((2*a*z+b)/(2*sqrt(a)))/(2*sqrt(a))$
 685
 686 /* Involving a*z^2+c -------------------------------------------------------- */
 687
 688 /* Problem 143: OK */
 689 integrate(d^(c+a*z^2),z),erf_representation:erfi,radexpand:all;
 690 sqrt(%pi)*d^c*erfi(sqrt(a)*sqrt(log(d))*z)/(2*sqrt(a)*sqrt(log(d)))$
 691
 692 /* Problem 144: OK */
 693 integrate(%e^(c+a*z^2),z),erf_representation:erfi,radexpand:all;
 694 sqrt(%pi)*%e^c*erfi(sqrt(a)*z)/(2*sqrt(a));
 695
 696 /* Involving a*z^2+b/z^2 ---------------------------------------------------- */
 697
 698 /* Problem 145: NEW 4 */
 699 diffcheck(integrate(d^(b/z^2+a*z^2),z),z,factor_radcan);
 700 d^(b/z^2+a*z^2);
 701
 702 /* Problem 146: NEW 4 */
 703 diffcheck(integrate(%e^(b/z^2+a*z^2),z),z,factor);
 704 %e^(b/z^2+a*z^2);
 705
 706 /* ----- Involving az^2+b/z^2+c --------------------------------------------- */
 707
 708 /* Problem 147: NEW 4 */
 709 diffcheck(integrate(d^(c+b/z^2+a*z^2),z),z,factor_radcan);
 710 d^(c+b/z^2+a*z^2);
 711
 712 /* Problem 148: NEW 4 */
 713 diffcheck(integrate(%e^(c+b/z^2+a*z^2),z),z,factor);
 714 %e^(c+b/z^2+a*z^2);
 715
 716 /* ----- Involving a*z+b*sqrt(z)+c ------------------------------------------ */
 717
 718 /* Problem 149: NEW 5
 719  * This integral is first transformed to an integral of type 5.
 720  */
 721 diffcheck(integrate(d^(c+a*z+sqrt(z)*b),z),z,radcan);
 722 d^(c+a*z+sqrt(z)*b);
 723
 724 /* Problem 150: NEW 5
 725  * This integral is first transformed to an integral of type 5.
 726 */
 727 diffcheck(integrate(%e^(c+a*z+sqrt(z)*b),z),z,factor), domain:real;
 728 %e^(c+a*z+sqrt(z)*b);
 729
 730 /* ----- Involving a*z+b*sqrt(z) -------------------------------------------- */
 731
 732 /* Problem 151: NEW 5 */
 733 diffcheck(integrate(d^(a*z+sqrt(z)*b),z),z,radcan);
 734 d^(a*z+sqrt(z)*b);
 735
 736 /* Problem 152: NEW 5 */
 737 diffcheck(integrate(%e^(a*z+sqrt(z)*b),z),z,factor), domain:real;
 738 %e^(a*z+sqrt(z)*b);
 739
 740 /* ----- Involving a*z^r+c -------------------------------------------------- */
 741
 742 /* Problem 153: NEW 1 */
 743 diffcheck(integrate(d^(c+a*z^r),z),z,radcan);
 744 d^(c+a*z^r);
 745
 746 /* Problem 154: NEW 1 */
 747 diffcheck(integrate(%e^(c+a*z^r),z),z,factor);
 748 %e^(c+a*z^r);
 749
 750 /* Problem 155: OK */
 751 integrate(%e^(c+a*z^2),z),erf_representation:erfi,radexpand:all;
 752 sqrt(%pi)*%e^c*erfi(sqrt(a)*z)/(2*sqrt(a))$
 753
 754 /* Problem 156: OK */
 755 integrate(%e^(c+a*sqrt(z)),z);
 756 2*(a*%e^c*sqrt(z)-%e^c)*%e^(a*sqrt(z))/a^2;
 757
 758 /* ----- Arguments involving exponential functions -------------------------- */
 759
 760 /* Problem 157: NEW 2 */
 761 integrate(a^b^z,z),gamma_expand:true,logcontract;
 762 expintegral_ei(log(a)*b^z)/log(b);
 763
 764 /* Problem 158: NEW 2 */
 765 integrate(%e^a^z,z),gamma_expand:true,logcontract,domain:complex;
 766 (expintegral_ei(a^z)+log(-1))/log(a);
 767
 768 /* Problem 159: NEW 2 */
 769 integrate(%e^%e^z,z),gamma_expand:true,logexpand:all;
 770 expintegral_ei(%e^z)+log(-1);
 771
 772 /* ----- Involving trigonometric functions ---------------------------------- */
 773
 774 /* Problem 160: NOUN */
 775 integrate(%e^tan(z),z);
 776 'integrate(%e^tan(z),z);
 777
 778 /* Problem 161: NOUN */
 779 integrate(%e^(a*tan(z)),z);
 780 'integrate(%e^(a*tan(z)),z);
 781
 782 /* Problem 162: NOUN */
 783 integrate(%e^cot(z),z);
 784 'integrate(%e^cot(z),z);
 785
 786 /* Problem 163: NOUN */
 787 integrate(%e^(a*cot(z)),z);
 788 'integrate(%e^(a*cot(z)),z);
 789
 790 /* ----- Involving hyperbolic functions ------------------------------------- */
 791
 792 /* Problem 164: NOUN */
 793 integrate(%e^tanh(z),z);
 794 'integrate(%e^tanh(z),z);
 795
 796 /* Problem 165: NOUN */
 797 integrate(%e^(a*tanh(z)),z);
 798 'integrate(%e^(a*tanh(z)),z);
 799
 800 /* Problem 166: NOUN */
 801 integrate(%e^coth(z),z);
 802 'integrate(%e^coth(z),z);
 803
 804 /* Problem 167: NOUN */
 805 integrate(%e^(a*coth(z)),z);
 806 'integrate(%e^(a*coth(z)),z);
 807
 808 /* ----- Involving inverse trigonometric functions -------------------------- */
 809
 810 /* Problem 168: NOUN */
 811 integrate(%e^asin(z),z);
 812 'integrate(%e^asin(z),z);
 813
 814 /* Problem 169: NOUN */
 815 integrate(%e^(a*asin(z)),z);
 816 'integrate(%e^(a*asin(z)),z);
 817
 818 /* Problem 170: NOUN */
 819 integrate(%e^acos(z),z);
 820 'integrate(%e^acos(z),z);
 821
 822 /* Problem 171: NOUN */
 823 integrate(%e^(a*acos(z)),z);
 824 'integrate(%e^(a*acos(z)),z);
 825
 826 /* Problem 172: NOUN */
 827 integrate(%e^atan(z),z);
 828 'integrate(%e^atan(z),z);
 829
 830 /* Problem 173: NOUN */
 831 integrate(%e^(a*atan(z)),z);
 832 'integrate(%e^(a*atan(z)),z);
 833
 834 /* Problem 174: NOUN */
 835 integrate(%e^acot(z),z);
 836 'integrate(%e^acot(z),z);
 837
 838 /* Problem 175: NOUN */
 839 integrate(%e^(a*acot(z)),z);
 840 'integrate(%e^(a*acot(z)),z);
 841
 842 /* Problem 176: NOUN */
 843 integrate(%e^acsc(z),z);
 844 'integrate(%e^acsc(z),z);
 845
 846 /* Problem 177: NOUN */
 847 integrate(%e^(a*acsc(z)),z);
 848 'integrate(%e^(a*acsc(z)),z);
 849
 850 /* Problem 178: NOUN */
 851 integrate(%e^asec(z),z);
 852 'integrate(%e^asec(z),z);
 853
 854 /* Problem 179: NOUN */
 855 integrate(%e^(a*asec(z)),z);
 856 'integrate(%e^(a*asec(z)),z);
 857
 858 /* Arguments invovling inverse hyperbolic functions ------------------------- */
 859
 860 /* Problem 180: NEW 12/2009 */
 861 integrate(%e^asinh(z),z);
 862 log(sqrt(z^2+1)+z)/2+z*sqrt(z^2+1)/2+z^2/2;
 863
 864 /* Problem 181: NOUN */
 865 integrate(%e^(a*asinh(z)),z);
 866 'integrate(%e^(a*asinh(z)),z);
 867
 868 /* Problem 182: NEW 12/2009 */
 869 integrate(%e^acosh(z),z);
 870 -log(2*sqrt(z^2-1)+2*z)/2+z*sqrt(z^2-1)/2+z^2/2;
 871
 872 /* Problem 183: NOUN */
 873 integrate(%e^(a*acosh(z)),z);
 874 'integrate(%e^(a*acosh(z)),z);
 875
 876 /* Problem 184: NOUN */
 877 integrate(%e^atan(z),z);
 878 'integrate(%e^atan(z),z);
 879
 880 /* Problem 185: NOUN */
 881 integrate(%e^(a*atan(z)),z);
 882 'integrate(%e^(a*atan(z)),z);
 883
 884 /* Problem 186: NOUN */
 885 integrate(%e^acot(z),z);
 886 'integrate(%e^acot(z),z);
 887
 888 /* Problem 187: NOUN */
 889 integrate(%e^(a*acot(z)),z);
 890 'integrate(%e^(a*acot(z)),z);
 891
 892 /* Problem 189: NEW 08/2010
 893  * This example works nicely for x>0. For z complex we get abs(z) expressions.
 894  */
 895 assume(x>0);
 896 [x>0];
 897 integrate(%e^acsch(x),x),radcan;
 898 -log(sqrt(x^2+1)+1)+2*log(x)+sqrt(x^2+1);
 899 forget(x>0);
 900 [x>0];
 901
 902 /* Problem 191: NOUN */
 903 integrate(%e^(a*acsch(z)),z);
 904 'integrate(%e^(a*acsch(z)),z);
 905
 906 /* Problem 193: NEW 12/2009 */
 907 assume(x>0);
 908 [x>0];
 909 integrate(%e^asech(x),x),ratsimp;
 910 -log((2*sqrt(1-x^2)+2)/x)+log(x)+sqrt(1-x^2)$
 911 forget(x>0);
 912 [x>0];
 913
 914 /* Problem 195: NOUN */
 915 integrate(%e^(a*asech(z)),z);
 916 'integrate(%e^(a*asech(z)),z);
 917
 918 /* ----- Involving z^n*d^(a*z^r+b*z) ---------------------------------------- */
 919
 920 /* Problem 196: NEW 5 */
 921 niceindices(integrate(z^n*d^(b*z+a*z^2),z));
 922 -a^(-n-1)*('sum(b^(n-i)*gamma_incomplete((i+1)/2,-log(d)*(2*a*z+b)^2/(4*a))
 923                        *(-1)^(i-n)*2^(i-n)*binomial(n,i)*(2*a*z+b)^(i+1)
 924                  /(-log(d)*(2*a*z+b)^2/a)^((i+1)/2),i,0,n))
 925  /(2*d^(b^2/(4*a)));
 926
 927 /* ----- Prove algorithm type 5 for some special case ----- */
 928
 929 diffcheck(integrate(z*d^(b*z+a*z^2),z),z,radcan);
 930 z*d^(b*z+a*z^2);
 931
 932 diffcheck(integrate(z^2*d^(b*z+a*z^2),z),z,radcan);
 933 z^2*d^(b*z+a*z^2);
 934
 935 diffcheck(integrate(z^3*d^(b*z+a*z^2),z),z,radcan);
 936 z^3*d^(b*z+a*z^2);
 937
 938 /* Problem 200: NEW 5 */
 939 niceindices(integrate(z^n*%e^(b*z+a*z^2),z));
 940 -a^(-n-1)*%e^-(b^2/(4*a))
 941          *('sum(b^(n-i)*gamma_incomplete((i+1)/2,-(2*a*z+b)^2/(4*a))
 942                        *(-1)^(i-n)*2^(i-n)*binomial(n,i)*(2*a*z+b)^(i+1)
 943                  /(-(2*a*z+b)^2/a)^((i+1)/2),i,0,n))
 944  /2;
 945
 946 /* ----- Prove algorithm type 5 for some special case ----- */
 947
 948 diffcheck(integrate(z*%e^(b*z+a*z^2),z),z,factor), domain:real;
 949 z*%e^(a*z^2+b*z)$
 950
 951 diffcheck(integrate(z^2*%e^(b*z+a*z^2),z),z,factor), domain:real;
 952 z^2*%e^(a*z^2+b*z)$
 953
 954 diffcheck(integrate(z^3*%e^(b*z+a*z^2),z),z,factor), domain:real;
 955 z^3*%e^(a*z^2+b*z)$
 956
 957 /* Problem 204: NEW 6 */
 958 niceindices(niceindices(integrate(z^n*d^(b*z+a*sqrt(z)),z)));
 959 log(d)^(-2*(n+1)+2*n+1)*2^(-n-1)
 960                        *('sum(4^j*binomial(n,j)
 961                                  *'sum(a^(2*n-j-i)*(-1)^(i-j)*binomial(j,i)
 962                                                   *(2*b*sqrt(z)+a)^(j+i)
 963                                                   *(a*log(d)
 964                                                      *gamma_incomplete(
 965                                                       (j+i+1)/2,
 966                                                       -log(d)
 967                                                        *(2*b*sqrt(z)+a)^2
 968                                                        /(4*b))*(2*b*sqrt(z)+a)
 969                                                    +2*b
 970                                                      *gamma_incomplete(
 971                                                       (j+i+2)/2,
 972                                                       -log(d)
 973                                                        *(2*b*sqrt(z)+a)^2
 974                                                        /(4*b))
 975                                                      *sqrt(
 976                                                       -log(d)
 977                                                        *(2*b*sqrt(z)+a)^2
 978                                                        /b))
 979                                         /(-log(d)*(2*b*sqrt(z)+a)^2/b)
 980                                          ^((j+i+1)/2),i,0,j),j,0,n))
 981  /(b^(2*(n+1))*d^(a^2/(4*b)));
 982
 983 /* --- For special cases n the integral is transformed to type 5 ------------ */
 984
 985 diffcheck(integrate(z*d^(b*z+a*sqrt(z)),z),z,radcan);
 986 z*d^(b*z+a*sqrt(z));
 987
 988 diffcheck(integrate(z^2*d^(b*z+a*sqrt(z)),z),z,radcan);
 989 z^2*d^(b*z+a*sqrt(z));
 990
 991 diffcheck(integrate(z^3*d^(b*z+a*sqrt(z)),z),z,radcan);
 992 z^3*d^(b*z+a*sqrt(z));
 993
 994 /* Problem 208: NEW 6 */
 995 niceindices(niceindices(integrate(z^n*%e^(b*z+a*sqrt(z)),z)));
 996 %e^-(a^2/(4*b))*2^(-n-1)
 997                *('sum(4^j*binomial(n,j)
 998                          *'sum(a^(2*n-j-i)*(-1)^(i-j)*binomial(j,i)
 999                                           *(2*b*sqrt(z)+a)^(j+i)
1000                                           *(a
1001                                            *gamma_incomplete(
1002                                             (j+i+1)/2,
1003                                             -(2*b*sqrt(z)+a)^2/(4*b))
1004                                            *(2*b*sqrt(z)+a)
1005                                            +2*b
1006                                              *gamma_incomplete(
1007                                               (j+i+2)/2,
1008                                               -(2*b*sqrt(z)+a)^2/(4*b))
1009                                              *sqrt(-(2*b*sqrt(z)+a)^2/b))
1010                                 /(-(2*b*sqrt(z)+a)^2/b)^((j+i+1)/2),i,0,j),j,
1011                       0,n))
1012  /b^(2*(n+1));
1013
1014 /* --- Again the problem is integrated with type 5 --- */
1015
1016 diffcheck(integrate(z*%e^(b*z+a*sqrt(z)),z),z,factor), domain:real;
1017 z*%e^(b*z+a*sqrt(z));
1018
1019 diffcheck(integrate(z^2*%e^(b*z+a*sqrt(z)),z),z,factor), domain:real;
1020 z^2*%e^(b*z+a*sqrt(z));
1021
1022 diffcheck(integrate(z^3*%e^(b*z+a*sqrt(z)),z),z,factor), domain:real;
1023 z^3*%e^(b*z+a*sqrt(z));
1024
1025 /* ----- Involving z^n*d^(a*z^r+b*z+c) -------------------------------------- */
1026
1027 /* Problem 212: NEW 5 */
1028 niceindices(integrate(z^n*d^(c+b*z+a*z^2),z));
1029 -a^(-n-1)*d^(c-b^2/(4*a))
1030          *('sum(b^(n-i)*gamma_incomplete((i+1)/2,-log(d)*(2*a*z+b)^2/(4*a))
1031                        *(-1)^(i-n)*2^(i-n)*binomial(n,i)*(2*a*z+b)^(i+1)
1032                  /(-log(d)*(2*a*z+b)^2/a)^((i+1)/2),i,0,n))
1033  /2;
1034
1035 /* Problem 213: NEW 5 */
1036 niceindices(integrate(z^n*%e^(c+b*z+a*z^2),z));
1037 -a^(-n-1)*%e^(c-b^2/(4*a))
1038          *('sum(b^(n-i)*gamma_incomplete((i+1)/2,-(2*a*z+b)^2/(4*a))
1039                        *(-1)^(i-n)*2^(i-n)*binomial(n,i)*(2*a*z+b)^(i+1)
1040                  /(-(2*a*z+b)^2/a)^((i+1)/2),i,0,n))
1041  /2;
1042
1043 /* Problem 214: NEW 6 */
1044 niceindices(niceindices(integrate(z^n*d^(c+b*z+a*sqrt(z)),z)));
1045 d^(c-a^2/(4*b))*log(d)^(-2*(n+1)+2*n+1)*2^(-n-1)
1046                *('sum(4^j*binomial(n,j)
1047                          *'sum(a^(2*n-j-i)*(-1)^(i-j)*binomial(j,i)
1048                                           *(2*b*sqrt(z)+a)^(j+i)
1049                                           *(a*log(d)
1050                                              *gamma_incomplete(
1051                                               (j+i+1)/2,
1052                                               -log(d)*(2*b*sqrt(z)+a)^2/(4*b))
1053                                              *(2*b*sqrt(z)+a)
1054                                            +2*b
1055                                              *gamma_incomplete(
1056                                               (j+i+2)/2,
1057                                               -log(d)*(2*b*sqrt(z)+a)^2/(4*b))
1058                                              *sqrt(
1059                                               -log(d)*(2*b*sqrt(z)+a)^2/b))
1060                                 /(-log(d)*(2*b*sqrt(z)+a)^2/b)^((j+i+1)/2),i,
1061                                0,j),j,0,n))
1062  /b^(2*(n+1));
1063
1064 /* Problem 215: NEW 6 */
1065 niceindices(niceindices(integrate(z^n*%e^(c+b*z+a*sqrt(z)),z)));
1066 %e^(c-a^2/(4*b))*2^(-n-1)
1067                 *('sum(4^j*binomial(n,j)
1068                           *'sum(a^(2*n-j-i)*(-1)^(i-j)*binomial(j,i)
1069                                            *(2*b*sqrt(z)+a)^(j+i)
1070                                            *(a
1071                                             *gamma_incomplete(
1072                                              (j+i+1)/2,
1073                                              -(2*b*sqrt(z)+a)^2/(4*b))
1074                                             *(2*b*sqrt(z)+a)
1075                                             +2*b
1076                                               *gamma_incomplete(
1077                                                (j+i+2)/2,
1078                                                -(2*b*sqrt(z)+a)^2/(4*b))
1079                                               *sqrt(-(2*b*sqrt(z)+a)^2/b))
1080                                  /(-(2*b*sqrt(z)+a)^2/b)^((j+i+1)/2),i,0,j),j,
1081                        0,n))
1082  /b^(2*(n+1));
1083
1084 /* ----- Involving z^(v-1)*d^(c+a*z^r) -------------------------------------- */
1085
1086 /* Problem 216: NEW 2 */
1087 integrate(z^(v-1)*d^(c+a*z^r),z);
1088 -d^c*gamma_incomplete(v/r,-a*log(d)*z^r)*z^v/(r*(-a*log(d)*z^r)^(v/r));
1089
1090 /* Problem 217: NEW 2 */
1091 integrate(z^(v-1)*%e^(c+a*z^r),z);
1092 -%e^c*gamma_incomplete(v/r,-a*z^r)*z^v/(r*(-a*z^r)^(v/r));
1093
1094 /* Problem 218: NEW 2 */
1095 integrate(z^(v-1)*d^(c+a*z^2),z);
1096 -d^c*gamma_incomplete(v/2,-a*log(d)*z^2)*z^v/(2*(-a*log(d)*z^2)^(v/2));
1097
1098 /* Problem 219: NEW 2 */
1099 integrate(z^(v-1)*%e^(c+a*z^2),z);
1100 -%e^c*gamma_incomplete(v/2,-a*z^2)*z^v/(2*(-a*z^2)^(v/2));
1101
1102 /* Problem 220: NEW 2 */
1103 integrate(z^(v-1)*d^(c+a*sqrt(z)),z);
1104 -2*d^c*gamma_incomplete(2*v,-a*log(d)*sqrt(z))*z^v/(-a*log(d)*sqrt(z))^(2*v);
1105
1106 /* Problem 221: NEW 2 */
1107 integrate(z^(v-1)*%e^(c+a*sqrt(z)),z);
1108 -2*%e^c*gamma_incomplete(2*v,-a*sqrt(z))*z^v/(-a*sqrt(z))^(2*v);
1109
1110 /* ----- Involving z^(2*n)*d^(a*z^2+b/Z^2) ---------------------------------- */
1111
1112 /* Problem 222: NOUN */
1113 integrate(z^(2*n)*d^(b/z^2+a*z^2),z);
1114 'integrate(d^(a*z^2+b/z^2)*z^(2*n),z);
1115
1116 /* Problem 223: NOUN */
1117 integrate(z^(2*n)*%e^(b/z^2+a*z^2),z);
1118 'integrate(z^(2*n)*%e^(a*z^2+b/z^2),z);
1119
1120 /* ----- Involving z^(2*n)*d^(a*z^2+b/Z^2+c) -------------------------------- */
1121
1122 /* Problem 224: NOUN */
1123 integrate(z^(2*n)*d^(c+b/z^2+a*z^2),z);
1124 'integrate(d^(a*z^2+b/z^2+c)*z^(2*n),z);
1125
1126 /* Problem 225: NOUN */
1127 integrate(z^(2*n)*%e^(c+b/z^2+a*z^2),z);
1128 'integrate(z^(2*n)*%e^(a*z^2+b/z^2+c),z);
1129
1130 /* ----- Involving powers of exp with arguments c*z and base a -------------- */
1131
1132 /* Problem 226: OK */
1133 integrate((a^(c*z))^v,z);
1134 (a^(c*z))^v/(c*v*log(a));
1135
1136 /* Problem 227: OK */
1137 integrate((a^z)^v,z);
1138 (a^z)^v/(log(a)*v);
1139
1140 /* ----- with arguments c*z and base %e ------------------------------------- */
1141
1142 /* The following examples 217 - 224 are not really correct, because Maxima
1143  * simplifies (%e^(c*z))^v -> %e^(v*c*z), which is not correct in general.
1144  */
1145
1146 /* Problem 228: OK */
1147 integrate((%e^(c*z))^v,z);
1148 (%e^(c*z))^v/(c*v);
1149
1150 /* Problem 229: OK */
1151 integrate((%e^z)^v,z);
1152 (%e^z)^v/v;
1153
1154 /* Problem 230: OK */
1155 integrate(sqrt(%e^(c*z)),z);
1156 2*sqrt(%e^(c*z))/c;
1157
1158 /* Problem 231: OK */
1159 integrate((%e^(c*z))^(3/2),z);
1160 2*(%e^(c*z))^(3/2)/(3*c);
1161
1162 /* Problem 232: OK */
1163 integrate((%e^(c*z))^(5/2),z);
1164 2*(%e^(c*z))^(5/2)/(5*c);
1165
1166 /* Problem 233: OK */
1167 integrate(1/sqrt(%e^(c*z)),z);
1168 -2/(c*sqrt(%e^(c*z)));
1169
1170 /* Problem 234: OK */
1171 integrate(1/(%e^(c*z))^(3/2),z);
1172 -2*(%e^(c*z))^(-3/2)/(3*c);
1173
1174 /* Problem 235: OK */
1175 integrate(1/(%e^(c*z))^(5/2),z);
1176 -2*(%e^(c*z))^(-5/2)/(5*c);
1177
1178 /* ----- with arguments c*z+b and base a ------------------------------------ */
1179
1180 /* Problem 236: OK */
1181 integrate((a^(c*z+b))^v,z);
1182 (a^(c*z+b))^v/(log(a)*c*v);
1183
1184 /* -----  with arguments c*z+b and base %e ---------------------------------- */
1185
1186 /* Problem 237: (OK) wrong simplification */
1187 integrate((%e^(c*z+b))^v,z);
1188 (%e^(c*z+b))^v/(c*v);
1189
1190 /* ----- with arguments c*z^r and base a ------------------------------------ */
1191
1192 /* Problem 238: NEW 1a */
1193 integrate((a^(c*z^r))^v,z);
1194 -gamma_incomplete(1/r,-log(a)*c*v*z^r)*(a^(c*z^r))^v*z
1195  /(a^(c*v*z^r)*r*(-log(a)*c*v*z^r)^(1/r));
1196
1197 /* Problem 239: (OK) wrong simplification
1198  * The examples 229 and 230 are not really correct.
1199  * e.g. (a^(c*z^2))^v is wrongly simplified to a^(v*c*z^2) and integrated.
1200  */
1201 integrate((a^(c*z^2))^v,z), domain:real;
1202 sqrt(%pi)*erf(sqrt(-log(a)*c*v)*z)/(2*sqrt(-log(a)*c*v))$
1203
1204 /* Problem 240: (OK) wrong simplification */
1205 integrate((a^(c*sqrt(z)))^v,z), domain:real;
1206 2*(log(a)*c*v*sqrt(z)-1)*%e^(log(a)*c*v*sqrt(z))/(log(a)^2*c^2*v^2)$
1207
1208 /* ----- with arguments c*z^r ----------------------------------------------- */
1209
1210 /* Problem 241: NEW 1a */
1211 integrate((%e^(c*z^r))^v,z);
1212 -gamma_incomplete(1/r,-c*v*z^r)*z*(%e^(c*z^r))^v*%e^-(c*v*z^r)
1213  /(r*(-c*v*z^r)^(1/r));
1214
1215 /* Problem 242: (OK) wrong simplification*/
1216 integrate((%e^(c*z^2))^v,z), domain:real;
1217 sqrt(%pi)*erf(sqrt(-c*v)*z)/(2*sqrt(-c*v))$
1218
1219 /* Problem 243: (OK) wrong simplification*/
1220 integrate((%e^(c*sqrt(z)))^v,z), domain:real;
1221 2*(c*v*sqrt(z)-1)*%e^(c*v*sqrt(z))/(c^2*v^2)$
1222
1223 /* ----- with arguments c*z^r+d and base a ---------------------------------- */
1224
1225 /* Problem 244: NEW 1a */
1226 integrate((a^(d+c*z^r))^v,z);
1227 -gamma_incomplete(1/r,-log(a)*c*v*z^r)*(a^(c*z^r+d))^v*z
1228  /(a^(c*v*z^r)*r*(-log(a)*c*v*z^r)^(1/r));
1229
1230 /* Problem 245: (OK) wrong simplification */
1231 integrate((a^(d+c*z^2))^v,z), domain:real;
1232 sqrt(%pi)*a^(d*v)*erf(sqrt(-log(a)*c*v)*z)/(2*sqrt(-log(a)*c*v))$
1233
1234 /* Problem 246: (OK) wrong simplification */
1235 integrate((a^(d+c*sqrt(z)))^v,z), domain:real;
1236 2*(a^(d*v)*log(a)*c*v*sqrt(z)-a^(d*v))*%e^(log(a)*c*v*sqrt(z))
1237  /(log(a)^2*c^2*v^2)$
1238
1239 /* ----- with arguments c*z^r+d --------------------------------------------- */
1240
1241 /* Problem 247: New 1a */
1242 integrate((%e^(d+c*z^r))^v,z);
1243 -gamma_incomplete(1/r,-c*v*z^r)*z*%e^-(c*v*z^r)*(%e^(c*z^r+d))^v
1244  /(r*(-c*v*z^r)^(1/r));
1245
1246 /* Problem 248: (OK) wrong simplification */
1247 integrate((%e^(d+c*z^2))^v,z), domain:real;
1248 sqrt(%pi)*%e^(d*v)*erf(sqrt(-c*v)*z)/(2*sqrt(-c*v))$
1249
1250 /* Problem 249: (OK) wrong simplification */
1251 integrate((%e^(d+c*sqrt(z)))^v,z), domain:real;
1252 2*(c*v*%e^(d*v)*sqrt(z)-%e^(d*v))*%e^(c*v*sqrt(z))/(c^2*v^2)$
1253
1254 /* ----- with arguments c*(z^r)^p and base a -------------------------------- */
1255
1256 /* Problem 250: NEW 1a
1257  * The minus factor is a workaround to get a comparable answer.
1258  */
1259 -integrate((a^(c*(z^r)^p))^v,z);
1260 gamma_incomplete(1/(p*r),-log(a)*c*v*(z^r)^p)*(a^(c*(z^r)^p))^v*z
1261  /(a^(c*v*(z^r)^p)*p*r*(-log(a)*c*v*(z^r)^p)^(1/(p*r)));
1262
1263 /* Problem 251: (OK) wrong simplification */
1264 integrate((a^(c*(z^r)^(1/r)))^v,z), domain:real;
1265 %e^(log(a)*c*v*z)/(log(a)*c*v)$
1266
1267 /* Problem 252: (OK) wrong simplification */
1268 integrate((a^(c*sqrt(z^2)))^v,z), domain:real;
1269 %e^(log(a)*c*v*z)/(log(a)*c*v)$
1270
1271 /* Problem 253: NEW 1a */
1272 integrate((%e^(c*(z^r)^p))^v,z);
1273 -gamma_incomplete(1/(p*r),-c*v*(z^r)^p)*z*(%e^(c*(z^r)^p))^v*%e^-(c*v*(z^r)^p)
1274  /(p*r*(-c*v*(z^r)^p)^(1/(p*r)));
1275
1276 /* Problem 254: (OK) wrong simplification */
1277 integrate((%e^(c*(z^r)^(1/r)))^v,z), domain:real;
1278 %e^(c*v*z)/(c*v)$
1279
1280 /* Problem 255: (OK) wrong simplification */
1281 integrate((%e^(c*sqrt(z^2)))^v,z), domain:real;
1282 %e^(c*v*z)/(c*v)$
1283
1284 /* ----- with arguments c*(z^r)^p+d and base a ------------------------------ */
1285
1286 /* Problem 256: NEW 1a */
1287 -integrate((a^(d+c*(z^r)^p))^v,z);
1288 gamma_incomplete(1/(p*r),-log(a)*c*v*(z^r)^p)*(a^(c*(z^r)^p+d))^v*z
1289  /(a^(c*v*(z^r)^p)*p*r*(-log(a)*c*v*(z^r)^p)^(1/(p*r)))$
1290
1291 /* Problem 257: (OK) wrong simplification */
1292 integrate((a^(d+c*(z^r)^(1/r)))^v,z), domain:real;
1293 a^(d*v)*%e^(log(a)*c*v*z)/(log(a)*c*v);
1294
1295 /* Problem 258: (OK) wrong simplification */
1296 integrate((a^(d+c*sqrt(z^2)))^v,z), domain:real;
1297 a^(d*v)*%e^(log(a)*c*v*z)/(log(a)*c*v);
1298
1299 /* Problem 259: NEW 1a */
1300 integrate((%e^(d+c*(z^r)^p))^v,z);
1301 -gamma_incomplete(1/(p*r),-c*v*(z^r)^p)*z*%e^-(c*v*(z^r)^p)
1302                                        *(%e^(c*(z^r)^p+d))^v
1303  /(p*r*(-c*v*(z^r)^p)^(1/(p*r)));
1304
1305 /* Problem 260: (OK) wrong simplification */
1306 integrate((%e^(d+c*(z^r)^(1/r)))^v,z), domain:real;
1307 %e^(c*v*z+d*v)/(c*v);
1308
1309 /* Problem 261: (OK) wrong simplification */
1310 integrate((%e^(d+c*sqrt(z^2)))^v,z), domain:real;
1311 %e^(c*v*z+d*v)/(c*v);
1312
1313 /* ----- with arguments a*z^2+b/z^2 ----------------------------------------- */
1314
1315 /* Problem 262: Noun */
1316 integrate((%e^(b/z^2+a*z^2))^v,z);
1317 'integrate((%e^(b/z^2+a*z^2))^v,z);
1318
1319 /* ----- with arguments a*z^2+b/z^2+c --------------------------------------- */
1320
1321 /* Problem 263: Noun */
1322 integrate((%e^(c+b/z^2+a*z^2))^v,z);
1323 'integrate((%e^(c+b/z^2+a*z^2))^v,z);
1324
1325 /* ----- Involving products of power functions ------------------------------ */
1326
1327 /* ----- a^(d*z)*h^(c*z) ---------------------------------------------------- */
1328
1329 /* Problem 265: OK
1330  * In this example we have a substitution of a^(d*z).
1331  * We get a question about the sign of an expression.
1332
1333   The expand(XXX,0,0) is due to a bug--the antiderivative is unsimplified.
1334  */
1335 (assume(notequal((c * log(h))/(d * log(a)),-1)),0);
1336 0$
1337
1338 expand(integrate(a^(d*z)*h^(c*z),z),0,0);
1339 (a^(d*z))^(c*log(h)/(log(a)*d)+1)/(log(a)*(c*log(h)/(log(a)*d)+1)*d)$
1340
1341 (forget(notequal((c * log(h))/(d * log(a)),-1)),0);
1342 0$
1343
1344 /* ----- a^(d*z)*h^(c*z+g) -------------------------------------------------- */
1345
1346 /* Problem 267: OK
1347  * But not for this example. We get no question about a sign.
1348  * With the help of radcan we get the expected answer.
1349  */
1350 integrate(a^(d*z)*h^(c*z+g),z),radcan;
1351 a^(d*z)*h^(c*z+g)/(c*log(h)+log(a)*d)$
1352
1353 /* ----- a^(d*z+e)*h^(c*z+g) ------------------------------------------------ */
1354
1355 /* Problem 268: OK */
1356 integrate(a^(d*z+e)*h^(c*z+g),z),radcan;
1357 a^(d*z+e)*h^(c*z+g)/(c*log(h)+log(a)*d)$
1358
1359 /* ----- a^(d*z)*h^(c*z^r) -------------------------------------------------- */
1360
1361 /* Problem 269: OK */
1362 -integrate(a^(d*z)*h^(c*z^2),z),factor;
1363 sqrt(%pi)*%e^-(log(a)^2*d^2/(4*c*log(h)))
1364           *erf((2*c*log(h)*z+log(a)*d)/(2*sqrt(-c*log(h))))
1365  /(2*sqrt(-c*log(h)));
1366
1367 /* Problem 270: NEW 8 */
1368 diffcheck(integrate(a^(d*z)*h^(c*sqrt(z)),z),z,radcan);
1369 a^(d*z)*h^(c*sqrt(z));
1370
1371 /* ----- a^(d*z+e)*h^(c*z^r) ------------------------------------------------ */
1372
1373 /* Problem 271: OK */
1374 -integrate(a^(d*z+e)*h^(c*z^2),z),factor;
1375 sqrt(%pi)*a^e*%e^-(log(a)^2*d^2/(4*c*log(h)))
1376           *erf((2*c*log(h)*z+log(a)*d)/(2*sqrt(-c*log(h))))
1377  /(2*sqrt(-c*log(h)));
1378
1379 /* Problem 272: NEW 8 */
1380 diffcheck(integrate(a^(d*z+e)*h^(c*sqrt(z)),z),z,radcan);
1381 a^(d*z+e)*h^(c*sqrt(z));
1382
1383 /* ----- a^(b*z^r)*h^(c*z^r) ------------------------------------------------ */
1384
1385 /* Problem 273: NEW 7 */
1386 diffcheck(integrate(a^(b*z^r)*h^(c*z^r),z),z,radcan);
1387 a^(b*z^r)*h^(c*z^r);
1388
1389 /* Problem 274: OK */
1390 integrate(a^(b*z^2)*h^(c*z^2),z);
1391 sqrt(%pi)*erf(sqrt(-c*log(h)-log(a)*b)*z)/(2*sqrt(-c*log(h)-log(a)*b));
1392
1393 /* Problem 275: OK */
1394 integrate(a^(b*sqrt(z))*h^(c*sqrt(z)),z),radcan, factor;
1395 2*a^(b*sqrt(z))*h^(c*sqrt(z))*(c*log(h)*sqrt(z)+log(a)*b*sqrt(z)-1)
1396  /(c*log(h)+log(a)*b)^2;
1397
1398 /* ----- a^(d*z)*h^(c*z^r+g) ------------------------------------------------ */
1399
1400 /* Problem 276: OK */
1401 integrate(a^(d*z)*h^(g+c*z^2),z),factor;
1402 -sqrt(%pi)*h^g*%e^-(log(a)^2*d^2/(4*c*log(h)))
1403           *erf((2*c*log(h)*z+log(a)*d)/(2*sqrt(-c*log(h))))
1404  /(2*sqrt(-c*log(h)));
1405
1406 /* Problem 277: NEW 8 */
1407 diffcheck(integrate(a^(d*z)*h^(g+c*sqrt(z)),z),z,radcan);
1408 a^(d*z)*h^(g+c*sqrt(z));
1409
1410 /* ----- a^(d*z+e)*h^(c*z^r+g) ---------------------------------------------- */
1411
1412 /* Problem 278: OK */
1413 integrate(a^(d*z+e)*h^(g+c*z^2),z);
1414 sqrt(%pi)*a^e*h^g*%e^-(log(a)^2*d^2/(4*c*log(h)))
1415                  *erf(sqrt(-c*log(h))*z-log(a)*d/(2*sqrt(-c*log(h))))
1416          /(2*sqrt(-c*log(h)));
1417
1418 /* Problem 279: NEW 8 */
1419 diffcheck(integrate(a^(d*z+e)*h^(g+c*sqrt(z)),z),z,radcan);
1420 a^(d*z+e)*h^(g+c*sqrt(z));
1421
1422 /* ----- a^(b*z^r)*h^(c*z^r+g) ---------------------------------------------- */
1423
1424 /* Problem 280: NEW 7 */
1425 diffcheck(integrate(a^(b*z^r)*h^(g+c*z^r),z),z,radcan);
1426 a^(b*z^r)*h^(g+c*z^r);
1427
1428 /* Problem 281: OK */
1429 integrate(a^(b*z^2)*h^(g+c*z^2),z);
1430 sqrt(%pi)*h^g*erf(sqrt(-c*log(h)-log(a)*b)*z)
1431          /(2*sqrt(-c*log(h)-log(a)*b));
1432
1433 /* Problem 282: OK */
1434 integrate(a^(b*sqrt(z))*h^(g+c*sqrt(z)),z),radcan,factor;
1435 2*a^(b*sqrt(z))*h^(c*sqrt(z)+g)*(c*log(h)*sqrt(z)+log(a)*b*sqrt(z)-1)
1436  /(c*log(h)+log(a)*b)^2;
1437
1438 /* ----- a^(b*z^r+e)*h^(c*z^r+g) -------------------------------------------- */
1439
1440 /* Problem 283: NEW 7 */
1441 expand(integrate(a^(e+b*z^r)*h^(g+c*z^r),z) -
1442 -a^e*h^g*gamma_incomplete(1/r,-(c*log(h)+log(a)*b)*z^r)*z
1443  /(r*(-(c*log(h)+log(a)*b)*z^r)^(1/r)));
1444 0;
1445
1446 /* Problem 284: OK */
1447 integrate(a^(e+b*z^2)*h^(g+c*z^2),z);
1448 sqrt(%pi)*a^e*h^g*erf(sqrt(-c*log(h)-log(a)*b)*z)
1449          /(2*sqrt(-c*log(h)-log(a)*b));
1450
1451 /* Problem 285: OK */
1452 integrate(a^(e+b*sqrt(z))*h^(g+c*sqrt(z)),z),radcan,factor;
1453 2*a^(b*sqrt(z)+e)*h^(c*sqrt(z)+g)*(c*log(h)*sqrt(z)+log(a)*b*sqrt(z)-1)
1454  /(c*log(h)+log(a)*b)^2;
1455
1456 /* ----- a^(d*z)*h^(c*z^r+f*z) ---------------------------------------------- */
1457
1458 /* Problem 286: OK */
1459 integrate(a^(d*z)*h^(f*z+c*z^2),z);
1460 sqrt(%pi)*%e^-((-f*log(h)-log(a)*d)^2/(4*c*log(h)))
1461                  *erf(sqrt(-c*log(h))*z+(-f*log(h)-log(a)*d)
1462                                         /(2*sqrt(-c*log(h))))
1463          /(2*sqrt(-c*log(h)));
1464
1465 /* Problem 287: NEW 8 */
1466 multthru(integrate(a^(d*z)*h^(f*z+c*sqrt(z)),z));
1467 a^(d*z)*h^(f*z+c*sqrt(z))/(f*log(h)+log(a)*d)
1468  -sqrt(%pi)*c*%e^-(c^2*log(h)^2/(4*(f*log(h)+log(a)*d)))*log(h)
1469            *erfi((2*(f*log(h)+log(a)*d)*sqrt(z)+c*log(h))
1470                   /(2*sqrt(f*log(h)+log(a)*d)))
1471   /(2*(f*log(h)+log(a)*d)^(3/2));
1472
1473 /* ----- a^(d*z+e)*h^(c*z^r+f*z) -------------------------------------------- */
1474
1475 /* Problem 288: OK */
1476 integrate(a^(d*z+e)*h^(f*z+c*z^2),z);
1477 sqrt(%pi)*a^e*%e^-((-f*log(h)-log(a)*d)^2/(4*c*log(h)))
1478                  *erf(sqrt(-c*log(h))*z+(-f*log(h)-log(a)*d)
1479                                         /(2*sqrt(-c*log(h))))
1480          /(2*sqrt(-c*log(h)));
1481
1482 /* Problem 289: NEW 8 */
1483 multthru(integrate(a^(d*z+e)*h^(f*z+c*sqrt(z)),z));
1484 a^(d*z+e)*h^(f*z+c*sqrt(z))/(f*log(h)+log(a)*d)
1485  -sqrt(%pi)*a^e*c*%e^-(c^2*log(h)^2/(4*(f*log(h)+log(a)*d)))*log(h)
1486            *erfi((2*(f*log(h)+log(a)*d)*sqrt(z)+c*log(h))
1487                   /(2*sqrt(f*log(h)+log(a)*d)))
1488   /(2*(f*log(h)+log(a)*d)^(3/2));
1489
1490 /* ----- a^(b*z^r)*h^(c*z^r+f*z) -------------------------------------------- */
1491
1492 /* Problem 290: OK */
1493 integrate(a^(b*z^2)*h^(f*z+c*z^2),z);
1494 sqrt(%pi)*%e^(f^2*log(h)^2/(4*(-c*log(h)-log(a)*b)))
1495                  *erf(sqrt(-c*log(h)-log(a)*b)*z
1496                        -f*log(h)/(2*sqrt(-c*log(h)-log(a)*b)))
1497          /(2*sqrt(-c*log(h)-log(a)*b));
1498
1499 /* Problem 291: NEW 9
1500  * This problem does not simplify to a nice expression in terms of the erf
1501  * function and a term a^b*sqrt(z)*h^(sqrt(z)+f*z), but it is correct.
1502  */
1503 diffcheck(integrate(a^(b*sqrt(z))*h^(f*z+c*sqrt(z)),z),z,radcan);
1504 a^(b*sqrt(z))*h^(f*z+c*sqrt(z));
1505
1506 /* ----- a^(b*z^r+e)*h^(c*z^r+f*z) ------------------------------------------ */
1507
1508 /* Problem 292: OK */
1509 integrate(a^(e+b*z^2)*h^(f*z+c*z^2),z);
1510 sqrt(%pi)*a^e*%e^(f^2*log(h)^2/(4*(-c*log(h)-log(a)*b)))
1511                  *erf(sqrt(-c*log(h)-log(a)*b)*z
1512                        -f*log(h)/(2*sqrt(-c*log(h)-log(a)*b)))
1513          /(2*sqrt(-c*log(h)-log(a)*b));
1514
1515 /* Problem 293: NEW 9 */
1516 diffcheck(integrate(a^(e+b*sqrt(z))*h^(f*z+c*sqrt(z)),z),z,radcan);
1517 a^(e+b*sqrt(z))*h^(f*z+c*sqrt(z));
1518
1519 /* ----- a^(b*z^r+d*z)*h^(c*z^r+f*z) ---------------------------------------- */
1520
1521 /* Problem 294: OK */
1522 integrate(a^(d*z+b*z^2)*h^(f*z+c*z^2),z);
1523 sqrt(%pi)*%e^((-f*log(h)-log(a)*d)^2/(4*(-c*log(h)-log(a)*b)))
1524                  *erf(sqrt(-c*log(h)-log(a)*b)*z
1525                        +(-f*log(h)-log(a)*d)/(2*sqrt(-c*log(h)-log(a)*b)))
1526          /(2*sqrt(-c*log(h)-log(a)*b));
1527
1528 /* Problem 295: NEW 9
1529  * Is this example correct? Verify it again.
1530  * The problem is that Maxima first does some substitution, the integral
1531  * is solvable too, but the result becomes more complicated.
1532  */
1533 multthru(integrate(a^(d*z+b*sqrt(z))*h^(f*z+c*sqrt(z)),z));
1534 gamma_incomplete(1,
1535                  -(log(h)*(2*f*sqrt(z)+c)+log(a)*(2*d*sqrt(z)+b))^2
1536                   /(4*(f*log(h)+log(a)*d)))
1537  *%e^-((c*log(h)+log(a)*b)^2/(4*(f*log(h)+log(a)*d)))
1538  /(f*log(h)+log(a)*d)
1539  -gamma_incomplete(1/2,
1540                    -(log(h)*(2*f*sqrt(z)+c)+log(a)*(2*d*sqrt(z)+b))^2
1541                     /(4*(f*log(h)+log(a)*d)))
1542   *%e^-((c*log(h)+log(a)*b)^2/(4*(f*log(h)+log(a)*d)))*(-c*log(h)-log(a)*b)
1543   *(log(h)*(2*f*sqrt(z)+c)+log(a)*(2*d*sqrt(z)+b))
1544   /(2*(f*log(h)+log(a)*d)^2
1545      *sqrt(-(log(h)*(2*f*sqrt(z)+c)+log(a)*(2*d*sqrt(z)+b))^2
1546             /(f*log(h)+log(a)*d)))$
1547
1548 /* ----- a^(d*z)*h^(c*z^r+f*z+g) -------------------------------------------- */
1549
1550 /* Problem 296: OK */
1551 integrate(a^(d*z)*h^(g+f*z+c*z^2),z);
1552 sqrt(%pi)*h^g*%e^-((-f*log(h)-log(a)*d)^2/(4*c*log(h)))
1553                  *erf(sqrt(-c*log(h))*z+(-f*log(h)-log(a)*d)
1554                                         /(2*sqrt(-c*log(h))))
1555          /(2*sqrt(-c*log(h)));
1556
1557 /* Problem 297: NEW 8 */
1558 multthru(integrate(a^(d*z)*h^(g+f*z+c*sqrt(z)),z));
1559 a^(d*z)*h^(f*z+c*sqrt(z)+g)/(f*log(h)+log(a)*d)
1560  -sqrt(%pi)*c*h^g*%e^-(c^2*log(h)^2/(4*(f*log(h)+log(a)*d)))*log(h)
1561            *erfi((2*(f*log(h)+log(a)*d)*sqrt(z)+c*log(h))
1562                   /(2*sqrt(f*log(h)+log(a)*d)))
1563   /(2*(f*log(h)+log(a)*d)^(3/2));
1564
1565 /* ----- a^(d*z+e)*h^(c*z^r+f*z+g) ------------------------------------------ */
1566
1567 /* Problem 298: OK */
1568 integrate(a^(d*z+e)*h^(g+f*z+c*z^2),z);
1569 sqrt(%pi)*a^e*h^g*%e^-((-f*log(h)-log(a)*d)^2/(4*c*log(h)))
1570                  *erf(sqrt(-c*log(h))*z+(-f*log(h)-log(a)*d)
1571                                         /(2*sqrt(-c*log(h))))
1572          /(2*sqrt(-c*log(h)));
1573
1574 /* Problem 299: NEW 8 */
1575 multthru(integrate(a^(d*z+e)*h^(g+f*z+c*sqrt(z)),z));
1576 a^(d*z+e)*h^(f*z+c*sqrt(z)+g)/(f*log(h)+log(a)*d)
1577  -sqrt(%pi)*a^e*c*h^g*%e^-(c^2*log(h)^2/(4*(f*log(h)+log(a)*d)))*log(h)
1578            *erfi((2*(f*log(h)+log(a)*d)*sqrt(z)+c*log(h))
1579                   /(2*sqrt(f*log(h)+log(a)*d)))
1580   /(2*(f*log(h)+log(a)*d)^(3/2));
1581
1582 /* ----- a^(b*z^r)*h^(c*z^r+f*z+g) ------------------------------------------ */
1583
1584 /* Problem 300: OK */
1585 integrate(a^(b*z^2)*h^(g+f*z+c*z^2),z);
1586 sqrt(%pi)*h^g*%e^(f^2*log(h)^2/(4*(-c*log(h)-log(a)*b)))
1587                  *erf(sqrt(-c*log(h)-log(a)*b)*z
1588                        -f*log(h)/(2*sqrt(-c*log(h)-log(a)*b)))
1589          /(2*sqrt(-c*log(h)-log(a)*b));
1590
1591 /* Problem 301: NEW 9 */
1592 multthru(integrate(a^(b*sqrt(z))*h^(g+f*z+c*sqrt(z)),z));
1593 gamma_incomplete(1,-(log(h)*(2*f*sqrt(z)+c)+log(a)*b)^2/(4*f*log(h)))
1594  *h^g*%e^-((c*log(h)+log(a)*b)^2/(4*f*log(h)))
1595  /(f*log(h))
1596  -gamma_incomplete(1/2,-(log(h)*(2*f*sqrt(z)+c)+log(a)*b)^2/(4*f*log(h)))
1597   *h^g*%e^-((c*log(h)+log(a)*b)^2/(4*f*log(h)))*(-c*log(h)-log(a)*b)
1598   *(log(h)*(2*f*sqrt(z)+c)+log(a)*b)
1599   /(2*f^2*log(h)^2*sqrt(-(log(h)*(2*f*sqrt(z)+c)+log(a)*b)^2/(f*log(h))));
1600
1601 /* ----- a^(b*z^r+e)*h^(c*z^r+f*z+g) ---------------------------------------- */
1602
1603 /* Problem 302: OK */
1604 integrate(a^(e+b*z^2)*h^(g+f*z+c*z^2),z);
1605 sqrt(%pi)*a^e*h^g*%e^(f^2*log(h)^2/(4*(-c*log(h)-log(a)*b)))
1606                  *erf(sqrt(-c*log(h)-log(a)*b)*z
1607                        -f*log(h)/(2*sqrt(-c*log(h)-log(a)*b)))
1608          /(2*sqrt(-c*log(h)-log(a)*b));
1609
1610 /* Problem 303: NEW 9 */
1611 multthru(integrate(a^(e+b*sqrt(z))*h^(g+f*z+c*sqrt(z)),z));
1612 gamma_incomplete(1,-(log(h)*(2*f*sqrt(z)+c)+log(a)*b)^2/(4*f*log(h)))
1613  *a^e*h^g*%e^-((c*log(h)+log(a)*b)^2/(4*f*log(h)))
1614  /(f*log(h))
1615  -gamma_incomplete(1/2,-(log(h)*(2*f*sqrt(z)+c)+log(a)*b)^2/(4*f*log(h)))
1616   *a^e*h^g*%e^-((c*log(h)+log(a)*b)^2/(4*f*log(h)))*(-c*log(h)-log(a)*b)
1617   *(log(h)*(2*f*sqrt(z)+c)+log(a)*b)
1618   /(2*f^2*log(h)^2*sqrt(-(log(h)*(2*f*sqrt(z)+c)+log(a)*b)^2/(f*log(h))));
1619
1620 /* ----- a^(b*z^r+d*z)*h^(c*z^r+f*z+g) -------------------------------------- */
1621
1622 /* Problem 304: OK */
1623 integrate(a^(d*z+b*z^2)*h^(g+f*z+c*z^2),z);
1624 sqrt(%pi)*h^g*%e^((-f*log(h)-log(a)*d)^2/(4*(-c*log(h)-log(a)*b)))
1625                  *erf(sqrt(-c*log(h)-log(a)*b)*z
1626                        +(-f*log(h)-log(a)*d)/(2*sqrt(-c*log(h)-log(a)*b)))
1627          /(2*sqrt(-c*log(h)-log(a)*b));
1628
1629 /* Problem 305: NEW 9 */
1630 multthru(integrate(a^(d*z+b*sqrt(z))*h^(g+f*z+c*sqrt(z)),z));
1631 gamma_incomplete(1,
1632                  -(log(h)*(2*f*sqrt(z)+c)+log(a)*(2*d*sqrt(z)+b))^2
1633                   /(4*(f*log(h)+log(a)*d)))
1634  *h^g*%e^-((c*log(h)+log(a)*b)^2/(4*(f*log(h)+log(a)*d)))
1635  /(f*log(h)+log(a)*d)
1636  -gamma_incomplete(1/2,
1637                    -(log(h)*(2*f*sqrt(z)+c)+log(a)*(2*d*sqrt(z)+b))^2
1638                     /(4*(f*log(h)+log(a)*d)))
1639   *h^g*%e^-((c*log(h)+log(a)*b)^2/(4*(f*log(h)+log(a)*d)))
1640   *(-c*log(h)-log(a)*b)*(log(h)*(2*f*sqrt(z)+c)+log(a)*(2*d*sqrt(z)+b))
1641   /(2*(f*log(h)+log(a)*d)^2
1642      *sqrt(-(log(h)*(2*f*sqrt(z)+c)+log(a)*(2*d*sqrt(z)+b))^2
1643             /(f*log(h)+log(a)*d)));
1644
1645 /* ----- a^(b*z^r+d*z+e)*h^(c*z^r+f*z+g) ------------------------------------ */
1646
1647 /* Problem 306: OK */
1648 integrate(a^(e+d*z+b*z^2)*h^(g+f*z+c*z^2),z);
1649 sqrt(%pi)*a^e*h^g*%e^((-f*log(h)-log(a)*d)^2/(4*(-c*log(h)-log(a)*b)))
1650                  *erf(sqrt(-c*log(h)-log(a)*b)*z
1651                        +(-f*log(h)-log(a)*d)/(2*sqrt(-c*log(h)-log(a)*b)))
1652          /(2*sqrt(-c*log(h)-log(a)*b));
1653
1654 /* Problem 307: NEW 9 */
1655 multthru(integrate(a^(e+d*z+b*sqrt(z))*h^(g+f*z+c*sqrt(z)),z));
1656 gamma_incomplete(1,
1657                  -(log(h)*(2*f*sqrt(z)+c)+log(a)*(2*d*sqrt(z)+b))^2
1658                   /(4*(f*log(h)+log(a)*d)))
1659  *a^e*h^g*%e^-((c*log(h)+log(a)*b)^2/(4*(f*log(h)+log(a)*d)))
1660  /(f*log(h)+log(a)*d)
1661  -gamma_incomplete(1/2,
1662                    -(log(h)*(2*f*sqrt(z)+c)+log(a)*(2*d*sqrt(z)+b))^2
1663                     /(4*(f*log(h)+log(a)*d)))
1664   *a^e*h^g*%e^-((c*log(h)+log(a)*b)^2/(4*(f*log(h)+log(a)*d)))
1665   *(-c*log(h)-log(a)*b)*(log(h)*(2*f*sqrt(z)+c)+log(a)*(2*d*sqrt(z)+b))
1666   /(2*(f*log(h)+log(a)*d)^2
1667      *sqrt(-(log(h)*(2*f*sqrt(z)+c)+log(a)*(2*d*sqrt(z)+b))^2
1668             /(f*log(h)+log(a)*d)));
1669
1670 /* ----- a^(d*z)*b^(e*z)*c^(f*z) -------------------------------------------- */
1671
1672 /* Problem 309: OK
1673  * This example does not simplify in a product of three power functions.
1674  */
1675
1676 (assume(notequal(ratsimp((log(c)*f+log(b)*e)/(log(a)*d)),-1)),0);
1677 0$
1678
1679 integrate(a^(d*z)*b^(e*z)*c^(f*z),z);
1680 (a^(d*z))^(log(c)*f/(log(a)*d)+log(b)*e/(log(a)*d)+1)/(log(a)*d*(log(c)*f/(log(a)*d)+log(b)*e/(log(a)*d)+1))$
1681
1682 (forget(notequal(log(c)*f/(log(a)*d)+log(b)*e/(log(a)*d),-1)),0);
1683 0$
1684
1685 /* ----- %e^(c*z)*(%e^(a*z))^v ---------------------------------------------- */
1686
1687 /* Problem 311: (OK) wrong simplification for complex integration variable
1688  * Change example to a real variable x.
1689  */
1690 integrate(%e^(c*x)*(%e^(a*x))^v,x);
1691 %e^(a*v*x+c*x)/(a*v+c)$
1692
1693 /* ----- %e^(c*z+d)*(%e^(a*z))^v -------------------------------------------- */
1694
1695 /* Problem 312: (OK) wrong simplification
1696  * Change example to a real variable x.
1697  */
1698 integrate(%e^(c*x+d)*(%e^(a*x))^v,x);
1699 %e^(a*v*x+c*x+d)/(a*v+c)$
1700
1701 /* ----- %e^(c*z)*(%e^(a*z+b))^v -------------------------------------------- */
1702
1703 /* Problem 313: (OK) wrong simplification
1704  * Change example to a real variable x.
1705  */
1706 integrate(%e^(c*x)*(%e^(a*x+b))^v,x);
1707 %e^(v*(a*x+b)+c*x)/(a*v+c)$
1708
1709 /* ----- %e^(c*z+d)*(%e^(a*z+b))^v ------------------------------------------ */
1710
1711 /* Problem 314: (OK) wrong simplifcation
1712  * Change example to a real variable x.
1713  */
1714 integrate(%e^(c*x+d)*(%e^(a*x+b))^v,x);
1715 %e^(v*(a*x+b)+c*x+d)/(a*v+c)$
1716
1717 /* ----- %e^(b*z^r)*(%e^(c*z))^v -------------------------------------------- */
1718
1719 /* Problem 315: (OK) wrong simplification */
1720 integrate(%e^(b*z^2)*(%e^(c*z))^v,z), domain:real;
1721 sqrt(%pi)*%e^-(c^2*v^2/(4*b))*erf(sqrt(-b)*z-c*v/(2*sqrt(-b)))/(2*sqrt(-b));
1722
1723 /* Problem 316: NEW 9-1 */
1724 diffcheck(integrate(%e^(b*sqrt(z))*(%e^(c*z))^v,z),z,factor_radcan),
1725    domain:complex;
1726 %e^(b*sqrt(z))*(%e^(c*z))^v;
1727
1728 /* ----- %e^(b*z^r+e)*(%e^(c*z))^v ------------------------------------------ */
1729
1730 /* Problem 317: (OK) wrong simplification */
1731 integrate(%e^(e+b*z^2)*(%e^(c*z))^v,z), domain:real;
1732 sqrt(%pi)*%e^(e-c^2*v^2/(4*b))*erf(sqrt(-b)*z-c*v/(2*sqrt(-b)))/(2*sqrt(-b));
1733
1734 /* Problem 318: NEW 9-1 */
1735 diffcheck(integrate(%e^(e+b*sqrt(z))*(%e^(c*z))^v,z),z,factor_radcan),
1736    domain:complex;
1737 %e^(e+b*sqrt(z))*(%e^(c*z))^v;
1738
1739 /* ----- %e^(b*z^r+d*z)*(%e^(c*z))^v ---------------------------------------- */
1740
1741 /* Problem 319: (OK) wrong simplification */
1742 integrate(%e^(d*z+b*z^2)*(%e^(c*z))^v,z), domain:real;
1743 sqrt(%pi)*%e^-((-c*v-d)^2/(4*b))*erf(sqrt(-b)*z+(-c*v-d)/(2*sqrt(-b)))
1744  /(2*sqrt(-b));
1745
1746 /* Problem 320: NEW 8-1 */
1747 diffcheck(integrate(%e^(d*z+b*sqrt(z))*(%e^(c*z))^v,z),z,factor);
1748 %e^(d*z+b*sqrt(z))*(%e^(c*z))^v;
1749
1750 /* ----- %e^(b*z^r+d*z+e)*(%e^(c*z))^v -------------------------------------- */
1751
1752 /* Problem 321: OK */
1753 integrate(%e^(e+d*z+b*z^2)*(%e^(c*z))^v,z), domain:real;
1754 sqrt(%pi)*%e^(e-(-c*v-d)^2/(4*b))*erf(sqrt(-b)*z+(-c*v-d)/(2*sqrt(-b)))
1755  /(2*sqrt(-b));
1756
1757 /* Problem 322: NEW 8-1 */
1758 diffcheck(integrate(%e^(e+d*z+b*sqrt(z))*(%e^(c*z))^v,z),z,factor);
1759 %e^(e+d*z+b*sqrt(z))*(%e^(c*z))^v;
1760
1761 /* ----- %e^(b*z^r)*(%e^(f*z+g))^v ------------------------------------------ */
1762
1763 /* Problem 323: OK */
1764 integrate(%e^(b*z^2)*(%e^(g+f*z))^v,z), domain:real;
1765 sqrt(%pi)*%e^(g*v-f^2*v^2/(4*b))*erf(sqrt(-b)*z-f*v/(2*sqrt(-b)))/(2*sqrt(-b));
1766
1767 /* Problem 324: NEW 9-1 */
1768 diffcheck(integrate(%e^(b*sqrt(z))*(%e^(g+f*z))^v,z),z,factor), domain:real;
1769 %e^(f*v*z+b*sqrt(z)+g*v)$
1770
1771 /* ----- %e^(b*z^r+e)*(%e^(f*z+g))^v ---------------------------------------- */
1772
1773 /* Problem 325: OK */
1774 integrate(%e^(e+b*z^2)*(%e^(g+f*z))^v,z), domain:real;
1775 sqrt(%pi)*%e^(-f^2*v^2/(4*b)+g*v+e)*erf(sqrt(-b)*z-f*v/(2*sqrt(-b)))
1776  /(2*sqrt(-b));
1777
1778 /* Problem 326: NEW 9-1 */
1779 diffcheck(integrate(%e^(e+b*sqrt(z))*(%e^(g+f*z))^v,z),z,factor), domain:real;
1780 %e^(f*v*z+b*sqrt(z)+g*v+e)$
1781
1782 /* ----- %e^(b*z^r+d*z)*(%e^(f*z+g))^v -------------------------------------- */
1783
1784 /* Problem 327: OK */
1785 integrate(%e^(d*z+b*z^2)*(%e^(g+f*z))^v,z), domain:real;
1786 sqrt(%pi)*%e^(g*v-(-f*v-d)^2/(4*b))*erf(sqrt(-b)*z+(-f*v-d)/(2*sqrt(-b)))
1787  /(2*sqrt(-b));
1788
1789 /* Problem 328: NEW 9-1
1790  * This example is not correct simplified.
1791  */
1792 diffcheck(integrate(%e^(d*z+b*sqrt(z))*(%e^(g+f*z))^v,z),z,radcan),
1793    domain:complex;
1794 (%e^(f*z))^v*%e^(d*z+b*sqrt(z)+g*v);
1795
1796 /* ----- %e^(b*z^r+d*z+e)*(%e^(f*z+g))^v ------------------------------------ */
1797
1798 /* Problem 329: OK */
1799 integrate(%e^(e+d*z+b*z^2)*(%e^(g+f*z))^v,z), domain:real;
1800 sqrt(%pi)*%e^(-(-f*v-d)^2/(4*b)+g*v+e)*erf(sqrt(-b)*z+(-f*v-d)/(2*sqrt(-b)))
1801  /(2*sqrt(-b));
1802
1803 /* Problem 330: NEW 9-1
1804  * This example is not correct simplified.
1805  */
1806 diffcheck(integrate(%e^(e+d*z+b*sqrt(z))*(%e^(g+f*z))^v,z),z,radcan),
1807    domain:complex;
1808 (%e^(f*z))^v*%e^(d*z+b*sqrt(z)+g*v+e);
1809
1810 /* ----- %e^(b*z)*(%e^(c*z^r))^v -------------------------------------------- */
1811
1812 /* Problem 331: OK */
1813 integrate(%e^(b*z)*(%e^(c*z^2))^v,z), domain:real;
1814 sqrt(%pi)*%e^-(b^2/(4*c*v))*erf(sqrt(-c*v)*z-b/(2*sqrt(-c*v)))/(2*sqrt(-c*v));
1815
1816 /* Problem 332: NEW 9-1 */
1817 diffcheck(integrate(%e^(b*z)*(%e^(c*sqrt(z)))^v,z),z,radcan),domain:complex;
1818 %e^(b*z)*(%e^(c*sqrt(z)))^v;
1819
1820 /* ----- %e^(d*z+e)*(%e^(c*z^r))^v ------------------------------------------ */
1821
1822 /* Problem 333: OK */
1823 integrate(%e^(d*z+e)*(%e^(c*z^2))^v,z), domain:real;
1824 sqrt(%pi)*%e^(e-d^2/(4*c*v))*erf(sqrt(-c*v)*z-d/(2*sqrt(-c*v)))
1825          /(2*sqrt(-c*v));
1826
1827 /* Problem 334: NEW 9-1 */
1828 diffcheck(integrate(%e^(d*z+e)*(%e^(c*sqrt(z)))^v,z),z,factor), domain:real;
1829 %e^(d*z+c*v*sqrt(z)+e)$
1830
1831 /* ----- %e^(b*z^r)*(%e^(c*z^r))^v ------------------------------------------ */
1832
1833 /* Problem 335: NEW 7-1 */
1834 diffcheck(integrate(%e^(b*z^r)*(%e^(c*z^r))^v,z),z,factor);
1835 %e^(b*z^r)*(%e^(c*z^r))^v;
1836
1837 /* Problem 336: OK */
1838 integrate(%e^(b*z^2)*(%e^(c*z^2))^v,z), domain:real;
1839 sqrt(%pi)*erf(sqrt(-c*v-b)*z)/(2*sqrt(-c*v-b));
1840
1841 /* Problem 337: OK */
1842 integrate(%e^(b*sqrt(z))*(%e^(c*sqrt(z)))^v,z), domain:real;
1843 2*((c*v+b)*sqrt(z)-1)*%e^(c*v*sqrt(z)+b*sqrt(z))/(c^2*v^2+2*b*c*v+b^2);
1844
1845 /* ----- %e^(b*z^r+e)*(%e^(c*z^r))^v ---------------------------------------- */
1846
1847 /* Problem 338: NEW 7-1 */
1848 diffcheck(integrate(%e^(e+b*z^r)*(%e^(c*z^r))^v,z),z,factor);
1849 %e^(e+b*z^r)*(%e^(c*z^r))^v;
1850
1851 /* Problem 339: OK */
1852 integrate(%e^(e+b*z^2)*(%e^(c*z^2))^v,z), domain:real;
1853 sqrt(%pi)*%e^e*erf(sqrt(-c*v-b)*z)/(2*sqrt(-c*v-b));
1854
1855 /* Problem 340: OK */
1856 integrate(%e^(e+b*sqrt(z))*(%e^(c*sqrt(z)))^v,z), domain:real;
1857 2*((c*%e^e*v+b*%e^e)*sqrt(z)-%e^e)*%e^(c*v*sqrt(z)+b*sqrt(z))
1858          /(c^2*v^2+2*b*c*v+b^2);
1859
1860 /* ----- %e^(b*z^r+d*z)*(%e^(c*z^r))^v -------------------------------------- */
1861
1862 /* Problem 341: OK */
1863 integrate(%e^(d*z+b*z^2)*(%e^(c*z^2))^v,z), domain:real;
1864 sqrt(%pi)*%e^(d^2/(4*(-c*v-b)))*erf(sqrt(-c*v-b)*z-d/(2*sqrt(-c*v-b)))
1865          /(2*sqrt(-c*v-b));
1866
1867 /* Problem 342: NEW 9-1 */
1868 diffcheck(integrate(%e^(d*z+b*sqrt(z))*(%e^(c*sqrt(z)))^v,z),z,radcan),
1869    domain:complex;
1870 %e^(d*z+b*sqrt(z))*(%e^(c*sqrt(z)))^v;
1871
1872 /* ----- %e^(b*z^r+d*z+e)*(%e^(c*z^r))^v ------------------------------------ */
1873
1874 /* Problem 343: OK */
1875 integrate(%e^(e+d*z+b*z^2)*(%e^(c*z^2))^v,z), domain:real;
1876 sqrt(%pi)*%e^(d^2/(4*(-c*v-b))+e)
1877                  *erf(sqrt(-c*v-b)*z-d/(2*sqrt(-c*v-b)))
1878          /(2*sqrt(-c*v-b));
1879
1880 /* Problem 344: NEW 9-1 */
1881 diffcheck(integrate(%e^(e+d*z+b*sqrt(z))*(%e^(c*sqrt(z)))^v,z),z,radcan),
1882    domain:complex;
1883 %e^(e+d*z+b*sqrt(z))*(%e^(c*sqrt(z)))^v;
1884
1885 /* ----- %e^(d*z)*(%e^(c*z^r+g))^v ------------------------------------------ */
1886
1887 /* Problem 345: OK */
1888 integrate(%e^(d*z)*(%e^(g+c*z^2))^v,z), domain:real;
1889 sqrt(%pi)*%e^(g*v-d^2/(4*c*v))*erf(sqrt(-c*v)*z-d/(2*sqrt(-c*v)))
1890          /(2*sqrt(-c*v));
1891
1892 /* Problem 346: NEW 9-1 */
1893 expand(integrate(%e^(d*z)*(%e^(g+c*sqrt(z)))^v,z)-
1894 (-(-gamma_incomplete(1/2,-(2*d*sqrt(z)+c*v)^2/(4*d))*c*v*(2*d*sqrt(z)+c*v)
1895  /(2*d^(3/2)*sqrt(-(2*d*sqrt(z)+c*v)^2/d))
1896  -gamma_incomplete(1,-(2*d*sqrt(z)+c*v)^2/(4*d))/sqrt(d))
1897  *(%e^(c*sqrt(z)+g))^v*%e^(d*z-(d*sqrt(z)+c*v)*sqrt(z)-c^2*v^2/(4*d))
1898  /sqrt(d)));
1899 0;
1900
1901 /* ----- %e^(d*z+e)*(%e^(c*z^r+g))^v ---------------------------------------- */
1902
1903 /* Problem 347: OK */
1904 integrate(%e^(d*z+e)*(%e^(g+c*z^2))^v,z), domain:real;
1905 sqrt(%pi)*%e^(g*v-d^2/(4*c*v)+e)*erf(sqrt(-c*v)*z-d/(2*sqrt(-c*v)))
1906          /(2*sqrt(-c*v));
1907
1908 /* Problem 348: NEW 9-1 */
1909 expand(integrate(%e^(d*z+e)*(%e^(g+c*sqrt(z)))^v,z)-
1910 (-(-gamma_incomplete(1/2,-(2*d*sqrt(z)+c*v)^2/(4*d))*c*v*(2*d*sqrt(z)+c*v)
1911  /(2*d^(3/2)*sqrt(-(2*d*sqrt(z)+c*v)^2/d))
1912  -gamma_incomplete(1,-(2*d*sqrt(z)+c*v)^2/(4*d))/sqrt(d))
1913  *(%e^(c*sqrt(z)+g))^v*%e^(d*z-(d*sqrt(z)+c*v)*sqrt(z)-c^2*v^2/(4*d)+e)
1914  /sqrt(d)));
1915 0;
1916
1917 /* ----- %e^(b*z^r)*(%e^(c*z^r+g))^v ---------------------------------------- */
1918
1919 /* Problem 349: NEW 7-1
1920  * The result is not correct simplified.
1921  */
1922 diffcheck(integrate(%e^(b*z^r)*(%e^(g+c*z^r))^v,z),z,radcan), domain:complex;
1923 (%e^(c*z^r))^v*%e^(b*z^r+g*v);
1924
1925 /* Problem 350: OK */
1926 integrate(%e^(b*z^2)*(%e^(g+c*z^2))^v,z), domain:real;
1927 sqrt(%pi)*%e^(g*v)*erf(sqrt(-c*v-b)*z)/(2*sqrt(-c*v-b));
1928
1929 /* Problem 351: OK */
1930 multthru(integrate(%e^(b*sqrt(z))*(%e^(g+c*sqrt(z)))^v,z)), domain:real;
1931 2*(c*v*%e^(g*v)+b*%e^(g*v))*sqrt(z)*%e^(c*v*sqrt(z)+b*sqrt(z))
1932  /(c^2*v^2+2*b*c*v+b^2)
1933  -2*%e^(c*v*sqrt(z)+b*sqrt(z)+g*v)/(c^2*v^2+2*b*c*v+b^2);
1934
1935 /* ----- %e^(b*z^r+e)*(%e^(c*z^r+g))^v -------------------------------------- */
1936
1937 /* Problem 352: NEW 7-1 */
1938 diffcheck(integrate(%e^(e+b*z^r)*(%e^(g+c*z^r))^v,z),z,factor);
1939 %e^(e+b*z^r)*(%e^(g+c*z^r))^v;
1940
1941 /* Problem 353: OK */
1942 integrate(%e^(e+b*z^2)*(%e^(g+c*z^2))^v,z), domain:real;
1943 sqrt(%pi)*%e^(g*v+e)*erf(sqrt(-c*v-b)*z)/(2*sqrt(-c*v-b));
1944
1945 /* Problem 354: OK */
1946 multthru(integrate(%e^(e+b*sqrt(z))*(%e^(g+c*sqrt(z)))^v,z)), domain:real;
1947 2*(c*v*%e^(g*v+e)+b*%e^(g*v+e))*sqrt(z)*%e^(c*v*sqrt(z)+b*sqrt(z))
1948  /(c^2*v^2+2*b*c*v+b^2)
1949  -2*%e^(c*v*sqrt(z)+b*sqrt(z)+g*v+e)/(c^2*v^2+2*b*c*v+b^2);
1950
1951 /* ----- %e^(b*z^r+d*z)*(%e^(c*z^r+g))^v ------------------------------------ */
1952
1953 /* Problem 355: OK */
1954 integrate(%e^(d*z+b*z^2)*(%e^(g+c*z^2))^v,z), domain:real;
1955 sqrt(%pi)*%e^(d^2/(4*(-c*v-b))+g*v)
1956                  *erf(sqrt(-c*v-b)*z-d/(2*sqrt(-c*v-b)))
1957          /(2*sqrt(-c*v-b));
1958
1959 /* Problem 356: NEW 9-1
1960  * Wrong simplified.
1961  */
1962 diffcheck(integrate(%e^(d*z+b*sqrt(z))*(%e^(g+c*sqrt(z)))^v,z),z,radcan),
1963    domain:complex;
1964 (%e^(c*sqrt(z)))^v*%e^(d*z+b*sqrt(z)+g*v);
1965
1966 /* ----- %e^(b*z^r+d*z+e)*(%e^(c*z^r+g))^v ---------------------------------- */
1967
1968 /* Problem 357: OK */
1969 integrate(%e^(e+d*z+b*z^2)*(%e^(g+c*z^2))^v,z), domain:real;
1970 sqrt(%pi)*%e^(d^2/(4*(-c*v-b))+g*v+e)
1971                  *erf(sqrt(-c*v-b)*z-d/(2*sqrt(-c*v-b)))
1972          /(2*sqrt(-c*v-b));
1973
1974 /* Problem 358: NEW 9-1 */
1975 diffcheck(integrate(%e^(e+d*z+b*sqrt(z))*(%e^(g+c*sqrt(z)))^v,z),z,radcan),
1976    domain:complex;
1977 (%e^(c*sqrt(z)))^v*%e^(d*z+b*sqrt(z)+g*v+e);
1978
1979 /* ----- %e^(d*z)*(%e^(c*z^r+f*z))^v ---------------------------------------- */
1980
1981 /* Problem 359: OK */
1982 integrate(%e^(d*z)*(%e^(f*z+c*z^2))^v,z), domain:real;
1983 sqrt(%pi)*%e^-((-f*v-d)^2/(4*c*v))
1984                  *erf(sqrt(-c*v)*z+(-f*v-d)/(2*sqrt(-c*v)))
1985          /(2*sqrt(-c*v));
1986
1987 /* Problem 360: NEW 8-1 */
1988 diffcheck(integrate(%e^(d*z)*(%e^(f*z+c*sqrt(z)))^v,z),z,factor);
1989 %e^(d*z)*(%e^(f*z+c*sqrt(z)))^v$
1990
1991 /* ----- %e^(d*z+e)*(%e^(c*z^r+f*z))^v -------------------------------------- */
1992
1993 /* Problem 361: OK */
1994 integrate(%e^(d*z+e)*(%e^(f*z+c*z^2))^v,z), domain:real;
1995 sqrt(%pi)*%e^(e-(-f*v-d)^2/(4*c*v))
1996                  *erf(sqrt(-c*v)*z+(-f*v-d)/(2*sqrt(-c*v)))
1997          /(2*sqrt(-c*v));
1998
1999 /* Problem 362: NEW 8-1 */
2000 integrate(%e^(d*z+e)*(%e^(f*z+c*sqrt(z)))^v,z);
2001 (2*sqrt(f*v+d)*%e^((2*f*v*sqrt(z)+2*d*sqrt(z)+c*v)^2/(4*(f*v+d)))
2002  -sqrt(%pi)*c*v*erfi((2*f*v*sqrt(z)+2*d*sqrt(z)+c*v)/(2*sqrt(f*v+d))))
2003  *%e^(d*z-(2*f*v*sqrt(z)+2*d*sqrt(z)+c*v)^2/(4*(f*v+d))+e)
2004  *(%e^(f*z+c*sqrt(z)))^v
2005  /(2*(f*v+d)^(3/2));
2006
2007 /* ----- %e^(b*z^r)*(%e^(c*z^r+f*z))^v -------------------------------------- */
2008
2009 /* Problem 363: OK */
2010 integrate(%e^(b*z^2)*(%e^(f*z+c*z^2))^v,z), domain:real;
2011 sqrt(%pi)*%e^(f^2*v^2/(4*(-c*v-b)))
2012                  *erf(sqrt(-c*v-b)*z-f*v/(2*sqrt(-c*v-b)))
2013          /(2*sqrt(-c*v-b));
2014
2015 /* Problem 364: NEW 9-1 */
2016 diffcheck(integrate(%e^(b*sqrt(z))*(%e^(f*z+c*sqrt(z)))^v,z),z,factor),domain:real;
2017 %e^(f*v*z+c*v*sqrt(z)+b*sqrt(z))$
2018
2019 /* ----- %e^(b*z^r+e)*(%e^(c*z^r+f*z))^v ------------------------------------ */
2020
2021 /* Problem 365: OK */
2022 integrate(%e^(e+b*z^2)*(%e^(f*z+c*z^2))^v,z), domain:real;
2023 sqrt(%pi)*%e^(f^2*v^2/(4*(-c*v-b))+e)
2024                  *erf(sqrt(-c*v-b)*z-f*v/(2*sqrt(-c*v-b)))
2025          /(2*sqrt(-c*v-b));
2026
2027 /* Problem 366: NEW 9-1 */
2028 diffcheck(integrate(%e^(e+b*sqrt(z))*(%e^(f*z+c*sqrt(z)))^v,z),z,factor), domain:real;
2029 %e^(f*v*z+c*v*sqrt(z)+b*sqrt(z)+e)$
2030
2031 /* ----- %e^(b*z^r+d*z)*(%e^(c*z^r+f*z))^v ---------------------------------- */
2032
2033 /* Problem 367: OK */
2034 integrate(%e^(d*z+b*z^2)*(%e^(f*z+c*z^2))^v,z), domain:real;
2035 sqrt(%pi)*%e^((-f*v-d)^2/(4*(-c*v-b)))
2036                  *erf(sqrt(-c*v-b)*z+(-f*v-d)/(2*sqrt(-c*v-b)))
2037          /(2*sqrt(-c*v-b));
2038
2039 /* Problem 368: NEW 9-1 */
2040 diffcheck(integrate(%e^(d*x+b*sqrt(z))*(%e^(f*z+c*sqrt(z)))^v,z),z,factor), domain:real;
2041 %e^(f*v*z+c*v*sqrt(z)+b*sqrt(z)+d*x)$
2042
2043 /* ----- %e^(b*z^r+d*z+e)*(%e^(c*z^r+f*z))^v -------------------------------- */
2044
2045 /* Problem 369: OK */
2046 integrate(%e^(e+d*z+b*z^2)*(%e^(f*z+c*z^2))^v,z), domain:real;
2047 sqrt(%pi)*%e^((-f*v-d)^2/(4*(-c*v-b))+e)
2048                  *erf(sqrt(-c*v-b)*z+(-f*v-d)/(2*sqrt(-c*v-b)))
2049          /(2*sqrt(-c*v-b));
2050
2051 /* Problem 370: NEW 9-1 */
2052 diffcheck(integrate(%e^(e+d*z+b*sqrt(z))*(%e^(f*z+c*sqrt(z)))^v,z),z,radcan),
2053    domain:complex;
2054 (%e^(c*sqrt(z)))^v*(%e^(f*z))^v*%e^(d*z+b*sqrt(z)+e);
2055
2056 /* ----- %e^(d*z)*(%e^(c*z^r+f*z+g))^v -------------------------------------- */
2057
2058 /* Problem 371: OK */
2059 integrate(%e^(d*z)*(%e^(g+f*z+c*z^2))^v,z), domain:real;
2060 sqrt(%pi)*%e^(g*v-(-f*v-d)^2/(4*c*v))
2061                  *erf(sqrt(-c*v)*z+(-f*v-d)/(2*sqrt(-c*v)))
2062          /(2*sqrt(-c*v));
2063
2064 /* Problem 372: NEW 8-1 */
2065 integrate(%e^(d*z)*(%e^(g+f*z+c*sqrt(z)))^v,z);
2066 (2*sqrt(f*v+d)*%e^((2*f*v*sqrt(z)+2*d*sqrt(z)+c*v)^2/(4*(f*v+d)))
2067  -sqrt(%pi)*c*v*erfi((2*f*v*sqrt(z)+2*d*sqrt(z)+c*v)/(2*sqrt(f*v+d))))
2068  *%e^(d*z-(2*f*v*sqrt(z)+2*d*sqrt(z)+c*v)^2/(4*(f*v+d)))
2069  *(%e^(f*z+c*sqrt(z)+g))^v
2070  /(2*(f*v+d)^(3/2));
2071
2072 /* ----- %e^(d*z+e)*(%e^(c*z^r+f*z+g))^v ------------------------------------ */
2073
2074 /* Problem 373: OK */
2075 integrate(%e^(d*z+e)*(%e^(g+f*z+c*z^2))^v,z), domain:real;
2076 sqrt(%pi)*%e^(-(-f*v-d)^2/(4*c*v)+g*v+e)
2077                  *erf(sqrt(-c*v)*z+(-f*v-d)/(2*sqrt(-c*v)))
2078          /(2*sqrt(-c*v));
2079
2080 /* Problem 374: NEW 8-1 */
2081 integrate(%e^(d*z+e)*(%e^(g+f*z+c*sqrt(z)))^v,z);
2082 (2*sqrt(f*v+d)*%e^((2*f*v*sqrt(z)+2*d*sqrt(z)+c*v)^2/(4*(f*v+d)))
2083  -sqrt(%pi)*c*v*erfi((2*f*v*sqrt(z)+2*d*sqrt(z)+c*v)/(2*sqrt(f*v+d))))
2084  *%e^(d*z-(2*f*v*sqrt(z)+2*d*sqrt(z)+c*v)^2/(4*(f*v+d))+e)
2085  *(%e^(f*z+c*sqrt(z)+g))^v
2086  /(2*(f*v+d)^(3/2));
2087
2088 /* ----- %e^(b*z^r)*(%e^(c*z^r+f*z+g))^v ------------------------------------ */
2089
2090 /* Problem 375: OK */
2091 integrate(%e^(b*z^2)*(%e^(g+f*z+c*z^2))^v,z), domain:real;
2092 sqrt(%pi)*%e^(f^2*v^2/(4*(-c*v-b))+g*v)
2093                  *erf(sqrt(-c*v-b)*z-f*v/(2*sqrt(-c*v-b)))
2094          /(2*sqrt(-c*v-b));
2095
2096 /* Problem 376: NEW 9-1 */
2097 diffcheck(integrate(%e^(b*sqrt(z))*(%e^(g+f*z+c*sqrt(z)))^v,z),z,radcan),
2098    domain:complex;
2099 (%e^(c*sqrt(z)))^v*%e^(b*sqrt(z)+g*v)*(%e^(f*z))^v;
2100
2101 /* ----- %e^(b*z^r+e)*(%e^(c*z^r+f*z+g))^v ---------------------------------- */
2102
2103 /* Problem 377: OK */
2104 integrate(%e^(e+b*z^2)*(%e^(g+f*z+c*z^2))^v,z), domain:real;
2105 sqrt(%pi)*%e^(f^2*v^2/(4*(-c*v-b))+g*v+e)
2106                  *erf(sqrt(-c*v-b)*z-f*v/(2*sqrt(-c*v-b)))
2107          /(2*sqrt(-c*v-b));
2108
2109 /* Problem 378: NEW 9-1 */
2110 diffcheck(integrate(%e^(e+b*sqrt(z))*(%e^(g+f*z+c*sqrt(z)))^v,z),z,radcan),
2111    domain:complex;
2112 (%e^(c*sqrt(z)))^v*%e^(b*sqrt(z)+g*v+e)*(%e^(f*z))^v;
2113
2114 /* ----- %e^(b*z^r+d*z)*(%e^(c*z^r+f*z+g))^v -------------------------------- */
2115
2116 /* Problem 379: OK */
2117 integrate(%e^(d*z+b*z^2)*(%e^(g+f*z+c*z^2))^v,z), domain:real;
2118 sqrt(%pi)*%e^((-f*v-d)^2/(4*(-c*v-b))+g*v)
2119                  *erf(sqrt(-c*v-b)*z+(-f*v-d)/(2*sqrt(-c*v-b)))
2120          /(2*sqrt(-c*v-b));
2121
2122 /* Problem 380: NEW 9-1 */
2123 diffcheck(integrate(%e^(d*z+b*sqrt(z))*(%e^(g+f*z+c*sqrt(z)))^v,z),z,radcan),
2124    domain:complex;
2125 (%e^(c*sqrt(z)))^v*(%e^(f*z))^v*%e^(d*z+b*sqrt(z)+g*v);
2126
2127 /* ----- %e^(b*z^r+d*z+e)*(%e^(c*z^r+f*z+g))^v ------------------------------ */
2128
2129 /* Problem 381: OK */
2130 integrate(%e^(e+d*z+b*z^2)*(%e^(g+f*z+c*z^2))^v,z), domain:real;
2131 sqrt(%pi)*%e^((-f*v-d)^2/(4*(-c*v-b))+g*v+e)
2132                  *erf(sqrt(-c*v-b)*z+(-f*v-d)/(2*sqrt(-c*v-b)))
2133          /(2*sqrt(-c*v-b));
2134
2135 /* Problem 382: NEW 9-1 */
2136 diffcheck(integrate(%e^(e+d*z+b*sqrt(z))*(%e^(g+f*z+c*sqrt(z)))^v,z),z,radcan),
2137    domain:complex;
2138 (%e^(c*sqrt(z)))^v*(%e^(f*z))^v*%e^(d*z+b*sqrt(z)+g*v+e);
2139
2140 /* ----- (%e^(c*z))^u*(%e^(a*z)^v ------------------------------------------- */
2141
2142 /* Problem 383: OK */
2143 integrate((%e^(c*x))^u*(%e^(a*x))^v,x);
2144 %e^(a*v*x+c*u*x)/(a*v+c*u)$
2145
2146 /* ----- (%e^(c*z))^u*(%e^(a*z+b)^v ----------------------------------------- */
2147
2148 /* Problem 384: OK */
2149 integrate((%e^(c*x))^u*(%e^(a*x+b))^v,x);
2150 %e^(v*(a*x+b)+c*u*x)/(a*v+c*u)$
2151
2152 /* ----- (%e^(c*z+d))^u*(%e^(a*z+b)^v --------------------------------------- */
2153
2154 /* Problem 385: OK */
2155 integrate((%e^(c*x+d))^u*(%e^(a*x+b))^v,x);
2156 %e^(u*(c*x+d)+v*(a*x+b))/(a*v+c*u)$
2157
2158 /* ----- (%e^(b*z))^u*(%e^(c*z^r)^v ----------------------------------------- */
2159
2160 /* Problem 386: OK */
2161 integrate((%e^(b*z))^u*(%e^(c*z^2))^v,z), domain:real;
2162 sqrt(%pi)*%e^-(b^2*u^2/(4*c*v))*erf(sqrt(-c*v)*z-b*u/(2*sqrt(-c*v)))
2163          /(2*sqrt(-c*v));
2164
2165 /* Problem 387: NEW 9-1 */
2166 diffcheck(integrate((%e^(b*z))^u*(%e^(c*sqrt(z)))^v,z),z,factor), domain:real;
2167 %e^(b*u*z+c*v*sqrt(z))$
2168
2169 /* ----- (%e^(d*z+e))^u*(%e^(c*z^r)^v --------------------------------------- */
2170
2171 /* Problem 388: OK */
2172 integrate((%e^(d*z+e))^u*(%e^(c*z^2))^v,z), domain:real;
2173 sqrt(%pi)*%e^(e*u-d^2*u^2/(4*c*v))
2174                  *erf(sqrt(-c*v)*z-d*u/(2*sqrt(-c*v)))
2175          /(2*sqrt(-c*v));
2176
2177 /* Problem 389: NEW 9-1 */
2178 diffcheck(integrate((%e^(d*z+e))^u*(%e^(c*sqrt(z)))^v,z),z,factor), domain:real;
2179 %e^(d*u*z+c*v*sqrt(z)+e*u)$
2180
2181 /* ----- (%e^(b*z^r))^u*(%e^(c*z^r+g)^v ------------------------------------- */
2182
2183 /* Problem 390: NEW 7-1 */
2184 diffcheck(integrate((%e^(b*z^r))^u*(%e^(c*z^r))^v,z),z,factor);
2185 (%e^(b*z^r))^u*(%e^(c*z^r))^v;
2186
2187 /* Problem 391: OK */
2188 integrate((%e^(b*z^2))^u*(%e^(c*z^2))^v,z), domain:real;
2189 sqrt(%pi)*erf(sqrt(-c*v-b*u)*z)/(2*sqrt(-c*v-b*u));
2190
2191 /* Problem 392: OK */
2192 integrate((%e^(b*sqrt(z)))^u*(%e^(c*sqrt(z)))^v,z), domain:real;
2193 2*((c*v+b*u)*sqrt(z)-1)*%e^(c*v*sqrt(z)+b*u*sqrt(z))
2194  /(c^2*v^2+2*b*c*u*v+b^2*u^2);
2195
2196 /* ----- (%e^(d*z))^u*(%e^(c*z^r+g)^v --------------------------------------- */
2197
2198 /* Problem 393: OK */
2199 integrate((%e^(d*z))^u*(%e^(g+c*z^2))^v,z), domain:real;
2200 sqrt(%pi)*%e^(g*v-d^2*u^2/(4*c*v))
2201                  *erf(sqrt(-c*v)*z-d*u/(2*sqrt(-c*v)))
2202          /(2*sqrt(-c*v));
2203
2204 /* Problem 394: NEW 9-1 */
2205 diffcheck(integrate((%e^(d*z))^u*(%e^(g+c*sqrt(z)))^v,z),z,factor), domain:real;
2206 %e^(d*u*z+c*v*sqrt(z)+g*v)$
2207
2208 /* ----- (%e^(d*z+e))^u*(%e^(c*z^r+g)^v ------------------------------------- */
2209
2210 /* Problem 395: OK */
2211 integrate((%e^(d*z+e))^u*(%e^(g+c*z^2))^v,z), domain:real;
2212 sqrt(%pi)*%e^(g*v-d^2*u^2/(4*c*v)+e*u)
2213                  *erf(sqrt(-c*v)*z-d*u/(2*sqrt(-c*v)))
2214          /(2*sqrt(-c*v));
2215
2216 /* Problem 396: NEW 9-1 */
2217 diffcheck(integrate((%e^(d*z+e))^u*(%e^(g+c*sqrt(z)))^v,z),z,factor), domain:real;
2218 %e^(d*u*z+c*v*sqrt(z)+g*v+e*u)$
2219
2220 /* ----- (%e^(b*z^r))^u*(%e^(c*z^r+g)^v ------------------------------------- */
2221
2222 /* Problem 397: NEW 7-1 */
2223 diffcheck(integrate((%e^(b*z^r))^u*(%e^(g+c*z^r))^v,z),z,factor);
2224 (%e^(b*z^r))^u*(%e^(g+c*z^r))^v;
2225
2226 /* Problem 398: OK */
2227 integrate((%e^(b*z^2))^u*(%e^(g+c*z^2))^v,z), domain:real;
2228 sqrt(%pi)*%e^(g*v)*erf(sqrt(-c*v-b*u)*z)/(2*sqrt(-c*v-b*u));
2229
2230 /* Problem 399: OK */
2231 integrate((%e^(b*sqrt(z)))^u*(%e^(g+c*sqrt(z)))^v,z), domain:real;
2232 2*((c*v*%e^(g*v)+b*u*%e^(g*v))*sqrt(z)-%e^(g*v))*%e^(c*v*sqrt(z)+b*u*sqrt(z))
2233  /(c^2*v^2+2*b*c*u*v+b^2*u^2);
2234
2235 /* ----- (%e^(b*z^r+e))^u*(%e^(c*z^r+g)^v ----------------------------------- */
2236
2237 /* Problem 400: NEW 7-1 */
2238 diffcheck(integrate((%e^(e+b*z^r))^u*(%e^(g+c*z^r))^v,z),z,factor);
2239 (%e^(e+b*z^r))^u*(%e^(g+c*z^r))^v;
2240
2241 /* Problem 401: OK */
2242 integrate((%e^(e+b*z^2))^u*(%e^(g+c*z^2))^v,z), domain:real;
2243 sqrt(%pi)*%e^(g*v+e*u)*erf(sqrt(-c*v-b*u)*z)/(2*sqrt(-c*v-b*u));
2244
2245 /* Problem 402: OK */
2246 integrate((%e^(e+b*sqrt(z)))^u*(%e^(g+c*sqrt(z)))^v,z), domain:real;
2247 2*((c*v*%e^(g*v+e*u)+b*u*%e^(g*v+e*u))*sqrt(z)-%e^(g*v+e*u))
2248  *%e^(c*v*sqrt(z)+b*u*sqrt(z))
2249  /(c^2*v^2+2*b*c*u*v+b^2*u^2);
2250
2251 /* ----- (%e^(d*z))^u*(%e^(c*z^r+f*z)^v ------------------------------------- */
2252
2253 /* Problem 403: OK */
2254 integrate((%e^(d*z))^u*(%e^(f*z+c*z^2))^v,z), domain:real;
2255 sqrt(%pi)*%e^-((-f*v-d*u)^2/(4*c*v))
2256                  *erf(sqrt(-c*v)*z+(-f*v-d*u)/(2*sqrt(-c*v)))
2257          /(2*sqrt(-c*v));
2258
2259 /* Problem 404: NEW 8-1 */
2260 integrate((%e^(d*z))^u*(%e^(f*z+c*sqrt(z)))^v,z);
2261 %e^-((2*f*v*sqrt(z)+2*d*u*sqrt(z)+c*v)^2/(4*(f*v+d*u)))
2262  *(2*sqrt(f*v+d*u)*%e^((2*f*v*sqrt(z)+2*d*u*sqrt(z)+c*v)^2/(4*(f*v+d*u)))
2263   -sqrt(%pi)*c*v*erfi((2*f*v*sqrt(z)+2*d*u*sqrt(z)+c*v)/(2*sqrt(f*v+d*u))))
2264  *(%e^(d*z))^u*(%e^(f*z+c*sqrt(z)))^v
2265  /(2*(f*v+d*u)^(3/2));
2266
2267 /* ----- (%e^(d*z+e))^u*(%e^(c*z^r+f*z)^v ----------------------------------- */
2268
2269 /* Problem 405: OK */
2270 integrate((%e^(e+d*z))^u*(%e^(f*z+c*z^2))^v,z), domain:real;
2271 sqrt(%pi)*%e^(e*u-(-f*v-d*u)^2/(4*c*v))
2272                  *erf(sqrt(-c*v)*z+(-f*v-d*u)/(2*sqrt(-c*v)))
2273          /(2*sqrt(-c*v));
2274
2275 /* Problem 406: NEW 8-1 */
2276 diffcheck(integrate((%e^(e+d*z))^u*(%e^(f*z+c*sqrt(z)))^v,z),z,factor);
2277 (%e^(e+d*z))^u*(%e^(f*z+c*sqrt(z)))^v;
2278
2279 /* ----- (%e^(b*z^r))^u*(%e^(c*z^r+f*z)^v ----------------------------------- */
2280
2281 /* Problem 407: OK */
2282 integrate((%e^(b*z^2))^u*(%e^(f*z+c*z^2))^v,z), domain:real;
2283 sqrt(%pi)*%e^(f^2*v^2/(4*(-c*v-b*u)))
2284                  *erf(sqrt(-c*v-b*u)*z-f*v/(2*sqrt(-c*v-b*u)))
2285          /(2*sqrt(-c*v-b*u));
2286
2287 /* Problem 408: NEW 9-1 */
2288 diffcheck(integrate((%e^(b*sqrt(z)))^u*(%e^(f*z+c*sqrt(z)))^v,z),z,factor), domain:real;
2289 %e^(f*v*z+c*v*sqrt(z)+b*u*sqrt(z))$
2290
2291 /* ----- (%e^(b*z^r+e))^u*(%e^(c*z^r+f*z)^v --------------------------------- */
2292
2293 /* Problem 409: OK */
2294 integrate((%e^(e+b*z^2))^u*(%e^(f*z+c*z^2))^v,z), domain:real;
2295 sqrt(%pi)*%e^(f^2*v^2/(4*(-c*v-b*u))+e*u)
2296                  *erf(sqrt(-c*v-b*u)*z-f*v/(2*sqrt(-c*v-b*u)))
2297          /(2*sqrt(-c*v-b*u));
2298
2299 /* Problem 410: NEW 9-1 */
2300 diffcheck(integrate((%e^(e+b*sqrt(z)))^u*(%e^(f*z+c*sqrt(z)))^v,z),z,factor), domain:real;
2301 %e^(f*v*z+c*v*sqrt(z)+b*u*sqrt(z)+e*u)$
2302
2303 /* ----- (%e^(b*z^r+d*z))^u*(%e^(c*z^r+f*z)^v ------------------------------- */
2304
2305 /* Problem 411: OK */
2306 integrate((%e^(d*z+b*z^2))^u*(%e^(f*z+c*z^2))^v,z), domain:real;
2307 sqrt(%pi)*%e^((-f*v-d*u)^2/(4*(-c*v-b*u)))
2308                  *erf(sqrt(-c*v-b*u)*z+(-f*v-d*u)/(2*sqrt(-c*v-b*u)))
2309          /(2*sqrt(-c*v-b*u));
2310
2311 /* Problem 412: NEW 9-1 */
2312 diffcheck(integrate((%e^(d*z+b*sqrt(z)))^u*(%e^(f*z+c*sqrt(z)))^v,z),z,radcan),
2313    domain:complex;
2314 (%e^(b*sqrt(z)))^u*(%e^(c*sqrt(z)))^v*(%e^(d*z))^u*(%e^(f*z))^v$
2315
2316 /* ----- (%e^(d*z))^u*(%e^(c*z^r+f*z+g)^v ----------------------------------- */
2317
2318 /* Problem 413: OK */
2319 integrate((%e^(d*z))^u*(%e^(g+f*z+c*z^2))^v,z), domain:real;
2320 sqrt(%pi)*%e^(g*v-(-f*v-d*u)^2/(4*c*v))
2321                  *erf(sqrt(-c*v)*z+(-f*v-d*u)/(2*sqrt(-c*v)))
2322          /(2*sqrt(-c*v));
2323
2324 /* Problem 414: NEW 8-1 */
2325 integrate((%e^(d*z))^u*(%e^(g+f*z+c*sqrt(z)))^v,z);
2326 %e^-((2*f*v*sqrt(z)+2*d*u*sqrt(z)+c*v)^2/(4*(f*v+d*u)))
2327  *(2*sqrt(f*v+d*u)*%e^((2*f*v*sqrt(z)+2*d*u*sqrt(z)+c*v)^2/(4*(f*v+d*u)))
2328   -sqrt(%pi)*c*v*erfi((2*f*v*sqrt(z)+2*d*u*sqrt(z)+c*v)/(2*sqrt(f*v+d*u))))
2329  *(%e^(d*z))^u*(%e^(f*z+c*sqrt(z)+g))^v
2330  /(2*(f*v+d*u)^(3/2));
2331
2332 /* ----- (%e^(d*z+e))^u*(%e^(c*z^r+f*z+g)^v --------------------------------- */
2333
2334 /* Problem 415: OK */
2335 integrate((%e^(e+d*z))^u*(%e^(g+f*z+c*z^2))^v,z), domain:real;
2336 sqrt(%pi)*%e^(-(-f*v-d*u)^2/(4*c*v)+g*v+e*u)
2337                  *erf(sqrt(-c*v)*z+(-f*v-d*u)/(2*sqrt(-c*v)))
2338          /(2*sqrt(-c*v));
2339
2340 /* Problem 416: NEW 8-1 */
2341 integrate((%e^(e+d*z))^u*(%e^(g+f*z+c*sqrt(z)))^v,z);
2342 %e^-((2*f*v*sqrt(z)+2*d*u*sqrt(z)+c*v)^2/(4*(f*v+d*u)))
2343  *(2*sqrt(f*v+d*u)*%e^((2*f*v*sqrt(z)+2*d*u*sqrt(z)+c*v)^2/(4*(f*v+d*u)))
2344   -sqrt(%pi)*c*v*erfi((2*f*v*sqrt(z)+2*d*u*sqrt(z)+c*v)/(2*sqrt(f*v+d*u))))
2345  *(%e^(d*z+e))^u*(%e^(f*z+c*sqrt(z)+g))^v
2346  /(2*(f*v+d*u)^(3/2));
2347
2348 /* ----- (%e^(b*z^r))^u*(%e^(c*z^r+f*z+g)^v --------------------------------- */
2349
2350 /* Problem 417: OK */
2351 integrate((%e^(b*z^2))^u*(%e^(g+f*z+c*z^2))^v,z), domain:real;
2352 sqrt(%pi)*%e^(f^2*v^2/(4*(-c*v-b*u))+g*v)
2353                  *erf(sqrt(-c*v-b*u)*z-f*v/(2*sqrt(-c*v-b*u)))
2354          /(2*sqrt(-c*v-b*u));
2355
2356 /* Problem 418: NEW 9-1 */
2357 diffcheck(integrate((%e^(b*sqrt(z)))^u*(%e^(g+f*z+c*sqrt(z)))^v,z),z,factor),domain:real;
2358 %e^(f*v*z+c*v*sqrt(z)+b*u*sqrt(z)+g*v)$
2359
2360 /* ----- (%e^(b*z^r+e))^u*(%e^(c*z^r+f*z+g)^v ------------------------------- */
2361
2362 /* Problem 419: OK */
2363 integrate((%e^(e+b*z^2))^u*(%e^(g+f*z+c*z^2))^v,z), domain:real;
2364 sqrt(%pi)*%e^(f^2*v^2/(4*(-c*v-b*u))+g*v+e*u)
2365                  *erf(sqrt(-c*v-b*u)*z-f*v/(2*sqrt(-c*v-b*u)))
2366          /(2*sqrt(-c*v-b*u));
2367
2368 /* Problem 420: NEW 9-1 */
2369 diffcheck(integrate((%e^(e+b*sqrt(z)))^u*(%e^(g+f*z+c*sqrt(z)))^v,z),z,factor),domain:real;
2370 %e^(f*v*z+c*v*sqrt(z)+b*u*sqrt(z)+g*v+e*u)$
2371
2372 /* ----- (%e^(b*z^r+d*z))^u*(%e^(c*z^r+f*z+g)^v ----------------------------- */
2373
2374 /* Problem 421: OK */
2375 integrate((%e^(d*z+b*z^2))^u*(%e^(g+f*z+c*z^2))^v,z), domain:real;
2376 sqrt(%pi)*%e^((-f*v-d*u)^2/(4*(-c*v-b*u))+g*v)
2377                  *erf(sqrt(-c*v-b*u)*z+(-f*v-d*u)/(2*sqrt(-c*v-b*u)))
2378          /(2*sqrt(-c*v-b*u));
2379
2380 /* Problem 422: NEW 9-1 */
2381 diffcheck(integrate((%e^(d*z+b*sqrt(z)))^u*(%e^(g+f*z+c*sqrt(z)))^v,z),z,radcan),
2382    domain:complex;
2383 %e^(g*v)*(%e^(b*sqrt(z)))^u*(%e^(c*sqrt(z)))^v*(%e^(d*z))^u*(%e^(f*z))^v;
2384
2385 /* ----- (%e^(b*z^r+d*z+e))^u*(%e^(c*z^r+f*z+g)^v --------------------------- */
2386
2387 /* Problem 423: OK */
2388 integrate((%e^(e+d*z+b*z^2))^u*(%e^(g+f*z+c*z^2))^v,z), domain:real;
2389 sqrt(%pi)*%e^((-f*v-d*u)^2/(4*(-c*v-b*u))+g*v+e*u)
2390                  *erf(sqrt(-c*v-b*u)*z+(-f*v-d*u)/(2*sqrt(-c*v-b*u)))
2391          /(2*sqrt(-c*v-b*u));
2392
2393 /* Problem 424: NEW 9-1 */
2394 diffcheck(integrate((%e^(e+d*z+b*sqrt(z)))^u*(%e^(g+f*z+c*sqrt(z)))^v,z),z,radcan),
2395    domain:complex;
2396 %e^(g*v+e*u)*(%e^(b*sqrt(z)))^u*(%e^(c*sqrt(z)))^v*(%e^(d*z))^u*(%e^(f*z))^v;
2397
2398 /* ----- Involving rational functions of the direct function ---------------- */
2399
2400 /* ----- Involving 1/(a+b*%e^(c*z)) ----------------------------------------- */
2401
2402 /* Problem 425: OK */
2403 integrate(1/(b*%e^(c*z)+a),z), domain:real;
2404 z/a-log(b*%e^(c*z)+a)/(a*c);
2405
2406 /* Problem 426: OK */
2407 integrate(1/(%e^(c*z)+1),z), domain:real;
2408 z-log(%e^(c*z)+1)/c;
2409
2410 /* Problem 427: OK */
2411 integrate(1/(1-%e^(c*z)),z), domain:real;
2412 z-log(%e^(c*z)-1)/c;
2413
2414 /* ----- Involving (a+b*%e^(c*z))^(-n)---------------------------------------- */
2415
2416 /* Problem 428: OK */
2417 integrate(1/(b*%e^(c*z)+a)^2,z), domain:real;
2418 -log(b*%e^(c*z)+a)/(a^2*c)+1/(c*(a*b*%e^(c*z)+a^2))+z/a^2;
2419
2420 /* Problem 429: OK */
2421 integrate(1/(%e^(c*z)+1)^2,z), domain:real;
2422 -log(%e^(c*z)+1)/c+1/(c*(%e^(c*z)+1))+z;
2423
2424 /* Problem 430: OK */
2425 integrate(1/(1-%e^(c*z))^2,z), domain:real;
2426 -log(%e^(c*z)-1)/c-1/(c*(%e^(c*z)-1))+z;
2427
2428 /* Problem 431: OK */
2429 integrate(1/(b*%e^(c*z)+a)^3,z), domain:real;
2430 -log(b*%e^(c*z)+a)/(a^3*c)+(2*b*%e^(c*z)+3*a)
2431                            /(c*(2*a^2*b^2*%e^(2*c*z)+4*a^3*b*%e^(c*z)+2*a^4))
2432                           +z/a^3;
2433
2434 /* Problem 432: OK */
2435 integrate(1/(b*%e^(c*z)+a)^4,z), domain:real;
2436 -log(b*%e^(c*z)+a)/(a^4*c)+(6*b^2*%e^(2*c*z)+15*a*b*%e^(c*z)+11*a^2)
2437                            /(c*(6*a^3*b^3*%e^(3*c*z)+18*a^4*b^2*%e^(2*c*z)
2438                                                     +18*a^5*b*%e^(c*z)+6*a^6))
2439                           +z/a^4;
2440
2441 /* ----- Involving %e^(d*z)/(a+b*%e^(c*z)) ---------------------------------- */
2442
2443 /* Problem 433: NOUN */
2444 integrate(%e^(d*z)/(b*%e^(c*z)+a),z);
2445 a*c
2446  *'integrate(%e^(d*z)/(b^2*(c-d)*%e^(2*c*z)+a*b*(2*c-2*d)*%e^(c*z)+a^2*(c-d)),
2447              z)
2448  -%e^(d*z)/(b*(c-d)*%e^(c*z)+a*(c-d));
2449
2450 /* Problem 435: OK */
2451 assume(a>0,b>0);
2452 [a>0,b>0];
2453
2454 integrate(%e^z/(a+b*%e^(2*z)),z), domain:real;
2455 atan(sqrt(b)*%e^z/sqrt(a))/(sqrt(a)*sqrt(b));
2456
2457 forget(a>0,b>0);
2458 [a>0,b>0];
2459
2460 /* Problem 437: OK */
2461 integrate(%e^(c*z)/(b*%e^(c*z)+a),z);
2462 log(b*%e^(c*z)+a)/(b*c);
2463
2464 /* Problem 438: OK */
2465 integrate((B*%e^(c*z)+A)/(b*%e^(c*z)+a),z), domain:real;
2466 log(b*%e^(c*z)+a)*(a*B-b*A)/(a*b*c)+z*A/a;
2467
2468 /* Problem 439: OK */
2469 integrate(%e^(2*c*z)/(b*%e^(c*z)+a),z);
2470 %e^(c*z)/(b*c)-a*log(b*%e^(c*z)+a)/(b^2*c);
2471
2472 /* Problem 441: OK */
2473 assume(a>0,b>0);
2474 [a>0,b>0];
2475
2476 integrate(%e^(c*z)/(b*%e^(2*c*z)+a),z);
2477 atan(b*%e^(c*z)/sqrt(a*b))/(sqrt(a*b)*c);
2478
2479 forget(a>0,b>0);
2480 [a>0,b>0];
2481
2482 /* Problem 444: OK */
2483 assume(a>0,b>0);
2484 [a>0,b>0];
2485
2486 integrate(%e^(c*z)/(b*%e^(3*c*z)+a),z), domain:real;
2487 -log(b^(2/3)*%e^(2*c*z)-a^(1/3)*b^(1/3)*%e^(c*z)+a^(2/3))
2488  /(6*a^(2/3)*b^(1/3)*c)
2489  +atan((2*b^(2/3)*%e^(c*z)-a^(1/3)*b^(1/3))/(sqrt(3)*a^(1/3)*b^(1/3)))
2490   /(sqrt(3)*a^(2/3)*b^(1/3)*c)
2491  +log((b^(1/3)*%e^(c*z)+a^(1/3))/b^(1/3))/(3*a^(2/3)*b^(1/3)*c);
2492
2493 forget(a>0,b>0);
2494 [a>0,b>0];
2495
2496 /* ----- Involving %e^(f*z)/(a+b*%e^(c*z))^-n ------------------------------- */
2497
2498 /* Problem 446: NOUN */
2499 integrate(%e^(f*z)/(b*c^(d*z)+a),z);
2500 'integrate(%e^(f*z)/(b*c^(d*z)+a),z);
2501 /* a*log(c)*d
2502    *'integrate(%e^(f*z)/(b^2*(log(c)*d-f)*%e^(2*log(c)*d*z)
2503                       +a*b*(2*log(c)*d-2*f)*%e^(log(c)*d*z)+a^2*(log(c)*d-f)),
2504              z)
2505  -%e^(f*z)/(b*(log(c)*d-f)*%e^(log(c)*d*z)+a*(log(c)*d-f));
2506 */
2507
2508 /* Problem 447: NOUN */
2509 integrate(%e^(d*z)/(b*%e^(c*z)+a)^2,z);
2510 2*a*c
2511  *'integrate(%e^(d*z)/(b^3*(2*c-d)*%e^(3*c*z)+a*b^2*(6*c-3*d)*%e^(2*c*z)
2512                                              +a^2*b*(6*c-3*d)*%e^(c*z)
2513                                              +a^3*(2*c-d)),z)
2514  -%e^(d*z)/(b^2*(2*c-d)*%e^(2*c*z)+a*b*(4*c-2*d)*%e^(c*z)+a^2*(2*c-d));
2515
2516 /* Problem 448: OK */
2517 integrate((B*%e^(c*z)+A)/(b*%e^(c*z)+a)^2,z), domain:real;
2518 (a*B-b*A)/(-c*(a*b^2*%e^(c*z)+a^2*b))-log(b*%e^(c*z)+a)*A/(a^2*c)+z*A/a^2$
2519
2520 /* Problem 449: OK */
2521 integrate((B*%e^(c*z)+A)/(b*%e^(c*z)+a)^3,z), domain:real;
2522 (-a^2*B+2*b^2*%e^(c*z)*A+3*a*b*A)/(c*(2*a^2*b^3*%e^(2*c*z)
2523                                      +4*a^3*b^2*%e^(c*z)+2*a^4*b))
2524  -log(b*%e^(c*z)+a)*A/(a^3*c)+z*A/a^3$
2525
2526 /* Problem 450: OK */
2527 integrate((C*%e^(2*c*z)+B*%e^(c*z)+A)/(b*%e^(c*z)+a)^3,z), domain:real;
2528 (%e^(c*z)*(2*a^2*b*C-2*b^3*A)+a^3*C+a^2*b*B-3*a*b^2*A)
2529  /(-c*(2*a^2*b^4*%e^(2*c*z)+4*a^3*b^3*%e^(c*z)+2*a^4*b^2))
2530  -log(b*%e^(c*z)+a)*A/(a^3*c)+z*A/a^3$
2531
2532 /* ----- Involving 1/(a*%e^(2*d*z)+b*%e^(d*z)+c)----------------------------- */
2533
2534 /* Problem 452: OK */
2535 assume(4*a*c-b^2>0);
2536 [4*a*c > b^2];
2537
2538 integrate(1/(c+b*%e^(d*z)+a*%e^(2*d*z)),z), domain:real;
2539 -log(a*%e^(2*d*z)+b*%e^(d*z)+c)/(2*c*d)-b
2540                                         *atan(
2541                                          (2*a*%e^(d*z)+b)/sqrt(4*a*c-b^2))
2542                                         /(c*sqrt(4*a*c-b^2)*d)+z/c$
2543
2544 forget(4*a*c-b^2>0);
2545 [4*a*c > b^2];
2546
2547 /* ----- Involving %e^(e*z)/(a*%e^(2*d*z)+b*%e^(d*z)+c)---------------------- */
2548
2549 /* Problem 454: NOUN */
2550 integrate(%e^(e*z)/(c+b*%e^(d*z)+a*%e^(2*d*z)),z);
2551 'integrate((b*d*%e^(d*z)+2*c*d)*%e^(e*z)
2552             /(a^2*(2*d-e)*%e^(4*d*z)+a*b*(4*d-2*e)*%e^(3*d*z)
2553                                     +(b^2*(2*d-e)+a*c*(4*d-2*e))*%e^(2*d*z)
2554                                     +b*c*(4*d-2*e)*%e^(d*z)+c^2*(2*d-e)),z)
2555  -%e^(e*z)/(a*(2*d-e)*%e^(2*d*z)+b*(2*d-e)*%e^(d*z)+c*(2*d-e));
2556
2557 /* Problem 456: OK */
2558 assume(4*a*c-b^2>0);
2559 [4*a*c > b^2];
2560
2561 integrate(%e^(2*d*z)/(c+b*%e^(d*z)+a*%e^(2*d*z)),z),logexpand;
2562 log(b*sqrt(%e^(2*d*z))+a*%e^(2*d*z)+c)/(2*a*d)
2563  -b*atan((2*a*sqrt(%e^(2*d*z))+b)/sqrt(4*a*c-b^2))/(a*sqrt(4*a*c-b^2)*d);
2564
2565 forget(4*a*c-b^2>0);
2566 [4*a*c > b^2];
2567
2568 /* ----- Other integrals ---------------------------------------------------- */
2569
2570 /* Problem 458: NOUN */
2571 integrate(6^z/(9^z*b+4^z*a),z);
2572 'integrate(6^z/(b*9^z+a*4^z),z);
2573
2574 /* Problem 459: OK */
2575 integrate((%e^(5*z)+%e^z)/(%e^(3*z)-%e^(2*z)+%e^z-1),z);
2576 -log(%e^(2*z)+1)/2-atan(%e^z)+log(%e^z-1)+(%e^(2*z)+2*%e^z)/2;
2577
2578 /* Problem 460: OK */
2579 integrate(1/(%e^(z/2)+%e^(z/3)+%e^(z/6)+1),z), domain:real;
2580 -3*log(%e^(z/3)+1)/2-3*log(%e^(z/6)+1)-3*atan(%e^(z/6))+z$
2581
2582 /* ----- Involving algebraic functions of the direct function --------------- */
2583
2584 /* ----- Involving (a+b*c^(d*z))^v ------------------------------------------ */
2585
2586 /* Problem 461: NOUN */
2587 integrate((b*c^(d*z)+a)^v,z);
2588 'integrate((b*c^(d*z)+a)^v,z);
2589
2590 /* Problem 463: OK */
2591 assume(a>0);
2592 [a>0];
2593
2594 integrate((b*c^(d*z)+a)^(1/2),z);
2595 2*sqrt(b*c^(d*z)+a)/(log(c)*d)+sqrt(a)*log(
2596                                        (2*sqrt(b*c^(d*z)+a)-2*sqrt(a))
2597                                         /(2*sqrt(b*c^(d*z)+a)+2*sqrt(a)))
2598                                /(log(c)*d);
2599 forget(a>0);
2600 [a>0];
2601
2602 /* Problem 465: NOUN */
2603 integrate((b*%e^(c*z)+a)^v,z);
2604 'integrate((b*%e^(c*z)+a)^v,z);
2605
2606 /* Problem 466: NOUN */
2607 integrate((a*%e^(c*z)+a)^v,z);
2608 'integrate((a*%e^(c*z)+a)^v,z);
2609
2610 /* Problem 467: NOUN */
2611 integrate((a-a*%e^(c*z))^v,z);
2612 'integrate((a-a*%e^(c*z))^v,z);
2613
2614 /* This assumptions is for the problems 457 - 468 */
2615 assume(a>0);
2616 [a>0];
2617
2618 /* Problem 469: OK */
2619 integrate((b*%e^(c*z)+a)^(5/2),z);
2620 a^(5/2)*log((2*sqrt(b*%e^(c*z)+a)-2*sqrt(a))/(2*sqrt(b*%e^(c*z)+a)+2*sqrt(a)))
2621  /c
2622  +(6*(b*%e^(c*z)+a)^(5/2)+10*a*(b*%e^(c*z)+a)^(3/2)+30*a^2*sqrt(b*%e^(c*z)+a))
2623   /(15*c);
2624
2625 /* Problem 470: OK */
2626 integrate((b*%e^(c*z)+a)^(3/2),z);
2627 a^(3/2)*log((2*sqrt(b*%e^(c*z)+a)-2*sqrt(a))
2628                      /(2*sqrt(b*%e^(c*z)+a)+2*sqrt(a)))
2629          /c
2630          +(2*(b*%e^(c*z)+a)^(3/2)+6*a*sqrt(b*%e^(c*z)+a))/(3*c);
2631
2632 /* Problem 471: OK */
2633 integrate((b*%e^(c*z)+a)^(1/2),z);
2634 sqrt(a)*log((2*sqrt(b*%e^(c*z)+a)-2*sqrt(a))
2635                      /(2*sqrt(b*%e^(c*z)+a)+2*sqrt(a)))
2636          /c
2637          +2*sqrt(b*%e^(c*z)+a)/c;
2638
2639 /* Problem 472: OK */
2640 integrate((a*%e^(c*z)+a)^(1/2),z);
2641 sqrt(a)*log((2*sqrt(a*%e^(c*z)+a)-2*sqrt(a))
2642                      /(2*sqrt(a*%e^(c*z)+a)+2*sqrt(a)))
2643          /c
2644          +2*sqrt(a*%e^(c*z)+a)/c;
2645
2646 /* Problem 473: OK */
2647 integrate((a-a*%e^(c*z))^(1/2),z);
2648 sqrt(a)*log((2*sqrt(a-a*%e^(c*z))-2*sqrt(a))
2649                      /(2*sqrt(a-a*%e^(c*z))+2*sqrt(a)))
2650          /c
2651          +2*sqrt(a-a*%e^(c*z))/c;
2652
2653 /* Problem 474: OK */
2654 integrate((b*%e^(c*z)+a)^((-1)/2),z);
2655 log((2*sqrt(b*%e^(c*z)+a)-2*sqrt(a))/(2*sqrt(b*%e^(c*z)+a)+2*sqrt(a)))
2656          /(sqrt(a)*c);
2657
2658 /* Problem 475: OK */
2659 integrate((a*%e^(c*z)+a)^((-1)/2),z);
2660 log((2*sqrt(a*%e^(c*z)+a)-2*sqrt(a))/(2*sqrt(a*%e^(c*z)+a)+2*sqrt(a)))
2661          /(sqrt(a)*c);
2662
2663 /* Problem 476: OK */
2664 integrate((a-a*%e^(c*z))^((-1)/2),z);
2665 log((2*sqrt(a-a*%e^(c*z))-2*sqrt(a))/(2*sqrt(a-a*%e^(c*z))+2*sqrt(a)))
2666          /(sqrt(a)*c);
2667
2668 /* Problem 477: OK */
2669 integrate((b*%e^(c*z)+a)^((-3)/2),z);
2670 log((2*sqrt(b*%e^(c*z)+a)-2*sqrt(a))/(2*sqrt(b*%e^(c*z)+a)+2*sqrt(a)))
2671          /(a^(3/2)*c)
2672          +2/(a*c*sqrt(b*%e^(c*z)+a));
2673
2674 /* Problem 478: OK */
2675 integrate((a*%e^(c*z)+a)^((-3)/2),z);
2676 log((2*sqrt(a*%e^(c*z)+a)-2*sqrt(a))/(2*sqrt(a*%e^(c*z)+a)+2*sqrt(a)))
2677          /(a^(3/2)*c)
2678          +2/(a*c*sqrt(a*%e^(c*z)+a));
2679
2680 /* Problem 479: OK */
2681 integrate((a-a*%e^(c*z))^((-3)/2),z);
2682 log((2*sqrt(a-a*%e^(c*z))-2*sqrt(a))/(2*sqrt(a-a*%e^(c*z))+2*sqrt(a)))
2683          /(a^(3/2)*c)
2684          +2/(a*c*sqrt(a-a*%e^(c*z)));
2685
2686 /* Problem 480: OK */
2687 integrate((b*%e^(c*z)+a)^((-5)/2),z);
2688 log((2*sqrt(b*%e^(c*z)+a)-2*sqrt(a))/(2*sqrt(b*%e^(c*z)+a)+2*sqrt(a)))
2689          /(a^(5/2)*c)
2690          +(6*(b*%e^(c*z)+a)+2*a)/(3*a^2*c*(b*%e^(c*z)+a)^(3/2));
2691
2692 /* Forget assumption for Problems 457 - 468 */
2693 forget(a>0);
2694 [a>0];
2695
2696 /* ----- Involving ((a+b*%e^(c*z))^v)^p ------------------------------------- */
2697
2698 /* Problem 482: NOUN */
2699 integrate(((b*%e^(c*z)+a)^v)^p,z);
2700 'integrate(((b*%e^(c*z)+a)^v)^p,z);
2701
2702 /* Assumption for Problems 472 - 475 */
2703 assume(a>0);
2704 [a>0];
2705
2706 /* Problem 484: OK */
2707 integrate(((b*%e^(c*z)+a)^5)^(1/2),z),radexpand:all;
2708 a^(5/2)*log((2*sqrt(b*%e^(c*z)+a)-2*sqrt(a))
2709                      /(2*sqrt(b*%e^(c*z)+a)+2*sqrt(a)))
2710          /c
2711          +(6*(b*%e^(c*z)+a)^(5/2)+10*a*(b*%e^(c*z)+a)^(3/2)
2712                                  +30*a^2*sqrt(b*%e^(c*z)+a))
2713           /(15*c);
2714
2715 /* Problem 485: OK */
2716 integrate(((b*%e^(c*z)+a)^3)^(1/2),z),radexpand:all;
2717 a^(3/2)*log((2*sqrt(b*%e^(c*z)+a)-2*sqrt(a))
2718                      /(2*sqrt(b*%e^(c*z)+a)+2*sqrt(a)))
2719          /c
2720          +(2*(b*%e^(c*z)+a)^(3/2)+6*a*sqrt(b*%e^(c*z)+a))/(3*c);
2721
2722 /* Problem 486: OK */
2723 integrate((b*%e^(c*z)+a)^(-3/2),z);
2724 log((2*sqrt(b*%e^(c*z)+a)-2*sqrt(a))/(2*sqrt(b*%e^(c*z)+a)+2*sqrt(a)))
2725          /(a^(3/2)*c)
2726          +2/(a*c*sqrt(b*%e^(c*z)+a));
2727
2728 /* Problem 487: OK */
2729 integrate((b*%e^(c*z)+a)^(-5/2),z);
2730 log((2*sqrt(b*%e^(c*z)+a)-2*sqrt(a))/(2*sqrt(b*%e^(c*z)+a)+2*sqrt(a)))
2731          /(a^(5/2)*c)
2732          +(6*(b*%e^(c*z)+a)+2*a)/(3*a^2*c*(b*%e^(c*z)+a)^(3/2));
2733
2734 /* Forget assumption for Problems 472 - 475 */
2735 forget(a>0);
2736 [a>0];
2737
2738 /* ----- Involving (a+b*c*%e^(d*z))^p*%e^(f*z) ------------------------------ */
2739
2740 /* Problem 489: NOUN */
2741 integrate((b*c^(d*z)+a)^p*%e^(f*z),z);
2742 'integrate((b*c^(d*z)+a)^p*%e^(f*z),z);
2743
2744 /* Problem 490: NOUN */
2745 integrate((b*%e^(c*z)+a)^p*%e^(f*z),z);
2746 'integrate((b*%e^(c*z)+a)^p*%e^(f*z),z);
2747
2748 /* Assumption for problems 480 - 490 */
2749 assume(notequal(p+1,0));
2750 [notequal(p,-1)];
2751
2752 /* Problem 492: OK */
2753 integrate((b*%e^(c*z)+a)^p*%e^(c*z),z);
2754 (b*%e^(c*z)+a)^(p+1)/(b*c*(p+1));
2755
2756 /* Problem 493: OK */
2757 integrate((a*%e^(c*z)+a)^p*%e^(c*z),z);
2758 (a*%e^(c*z)+a)^(p+1)/(a*c*(p+1));
2759
2760 /* Problem 494: OK */
2761 integrate((a-a*%e^(c*z))^p*%e^(c*z),z);
2762 -(a-a*%e^(c*z))^(p+1)/(a*c*(p+1));
2763
2764 /* Problem 495: OK */
2765 integrate((b*%e^(c*z)+a)^(1/2)*%e^(c*z),z);
2766 2*(b*%e^(c*z)+a)^(3/2)/(3*b*c);
2767
2768 /* Problem 496: OK */
2769 integrate((a*%e^(c*z)+a)^(1/2)*%e^(c*z),z);
2770 2*(a*%e^(c*z)+a)^(3/2)/(3*a*c);
2771
2772 /* Problem 497: OK */
2773 integrate((a-a*%e^(c*z))^(1/2)*%e^(c*z),z);
2774 -2*(a-a*%e^(c*z))^(3/2)/(3*a*c);
2775
2776 /* Problem 498: OK */
2777 integrate((b*%e^(c*z)+a)^((-1)/2)*%e^(c*z),z);
2778 2*sqrt(b*%e^(c*z)+a)/(b*c);
2779
2780 /* Problem 499: OK */
2781 integrate((a*%e^(c*z)+a)^((-1)/2)*%e^(c*z),z);
2782 2*sqrt(a*%e^(c*z)+a)/(a*c);
2783
2784 /* Problem 500: OK */
2785 integrate((a-a*%e^(c*z))^((-1)/2)*%e^(c*z),z);
2786 -2*sqrt(a-a*%e^(c*z))/(a*c);
2787
2788 /* Problem 501: OK */
2789 integrate((b*%e^(c*z)+a)^((-3)/2)*%e^(c*z),z);
2790 -2/(b*c*sqrt(b*%e^(c*z)+a));
2791
2792 /* Problem 502: OK */
2793 integrate((b*%e^(c*z)+a)^((-5)/2)*%e^(c*z),z);
2794 -2/(3*b*c*(b*%e^(c*z)+a)^(3/2));
2795
2796 /* Forget assumption for problems 480 - 490 */
2797 forget(notequal(p+1,0));
2798 [notequal(p,-1)];
2799
2800 /* ----- Involving ((a+b*c*%e^(c*z))^v)^p*%e^(d*z) -------------------------- */
2801
2802 /* Problem 504: NOUN */
2803 integrate(((b*%e^(c*z)+a)^v)^p*%e^(d*z),z);
2804 'integrate(((b*%e^(c*z)+a)^v)^p*%e^(d*z),z);
2805
2806 /* Problem 505: OK */
2807 integrate(((b*%e^(c*z)+a)^5)^(1/2)*%e^(c*z),z),domain:real;
2808 2*(b*%e^(c*z)+a)^(7/2)/(7*b*c)$
2809
2810 /* Problem 506: OK */
2811 integrate(((b*%e^(c*z)+a)^3)^(1/2)*%e^(c*z),z),domain:real;
2812 2*(b*%e^(c*z)+a)^(5/2)/(5*b*c)$
2813
2814 /* Problem 507: OK */
2815 integrate((b*%e^(c*z)+a)^(-3/2)*%e^(c*z),z);
2816 -2/(b*c*sqrt(b*%e^(c*z)+a));
2817
2818 /* Problem 508: OK */
2819 integrate((a*%e^(c*z)+a)^(-3/2)*%e^(c*z),z);
2820 -2/(a*c*sqrt(a*%e^(c*z)+a));
2821
2822 /* Problem 509: OK */
2823 integrate((a-a*%e^(c*z))^(-3/2)*%e^(c*z),z);
2824 2/(a*c*sqrt(a-a*%e^(c*z)));
2825
2826 /* Problem 510: OK */
2827 integrate((b*%e^(c*z)+a)^(-5/2)*%e^(c*z),z);
2828 -2/(3*b*c*(b*%e^(c*z)+a)^(3/2));
2829
2830 /* ----- Involving (a+b*%e^(c*z))^p*(%e^(d*z))^v ---------------------------- */
2831
2832 /* Problem 511: NOUN */
2833 integrate((b*%e^(c*z)+a)^p*(%e^(d*z))^v,z);
2834 'integrate((b*%e^(c*z)+a)^p*(%e^(d*z))^v,z);
2835
2836 /* Problem 512: NOUN */
2837 integrate((b*%e^(c*z)+a)^p*(%e^(c*z))^v,z);
2838 'integrate((%e^(c*z))^v*(b*%e^(c*z)+a)^p,z);
2839
2840 /* Problem 514: OK */
2841 assume(a>0,b>0);
2842 [a>0,b>0];
2843
2844 integrate((%e^(c*z))^(1/2)/(b*%e^(c*z)+a),z);
2845 2*atan(b*sqrt(%e^(c*z))/sqrt(a*b))/(sqrt(a*b)*c);
2846
2847 forget(a>0,b>0);
2848 [a>0,b>0];
2849
2850 /* ----- Involving (a+b*%e^(c*z))^p and rational function of %e^(c*z) ------- */
2851
2852 /* Problem 516: NOUN */
2853 integrate(e^(q*z)*(b*%e^(c*z)+a)^p/(e*%e^(c*z)+d),z);
2854 'integrate(e^(q*z)*(b*%e^(c*z)+a)^p/(e*%e^(c*z)+d),z);
2855
2856 /* Problem 517: NOUN */
2857 integrate((b*%e^(c*z)+a)^p/(e*%e^(c*z)+d),z);
2858 'integrate((b*%e^(c*z)+a)^p/(e*%e^(c*z)+d),z);
2859
2860 assume(a>0,e>0,(a*e-b*d)>0);
2861 [a > 0,e>0,a*e>b*d];
2862
2863 /* Problem 519: NEW 08-2010 */
2864 integrate((b*%e^(c*z)+a)^(1/2)/(e*%e^(c*z)+d),z);
2865 sqrt(a)*log((2*sqrt(b*%e^(c*z)+a)-2*sqrt(a))/(2*sqrt(b*%e^(c*z)+a)+2*sqrt(a)))
2866  /(c*d)
2867  -(a*e-b*d)*log((2*e*sqrt(b*%e^(c*z)+a)-2*sqrt(e*(a*e-b*d)))
2868                  /(2*e*sqrt(b*%e^(c*z)+a)+2*sqrt(e*(a*e-b*d))))
2869   /(c*d*sqrt(e*(a*e-b*d)))$
2870
2871 /* Problem 520: NEW 08-2010 */
2872 integrate((b*%e^(c*z)+a)^((-1)/2)/(e*%e^(c*z)+d),z);
2873 log((2*sqrt(b*%e^(c*z)+a)-2*sqrt(a))/(2*sqrt(b*%e^(c*z)+a)+2*sqrt(a)))
2874  /(sqrt(a)*c*d)
2875  -e*log((2*e*sqrt(b*%e^(c*z)+a)-2*sqrt(e*(a*e-b*d)))
2876          /(2*e*sqrt(b*%e^(c*z)+a)+2*sqrt(e*(a*e-b*d))))
2877   /(c*d*sqrt(e*(a*e-b*d)))$
2878
2879 /* Problem 521: NEW 08-2010 */
2880 integrate(%e^(c*z)*(b*%e^(c*z)+a)^((-1)/2)/(e*%e^(c*z)+d),z);
2881 log((2*e*sqrt(b*%e^(c*z)+a)-2*sqrt(e*(a*e-b*d)))
2882      /(2*e*sqrt(b*%e^(c*z)+a)+2*sqrt(e*(a*e-b*d))))
2883  /(c*sqrt(e*(a*e-b*d)))$
2884
2885 forget(a>0,e>0,(a*e-b*d)>0);
2886 [a > 0,e>0,a*e>b*d];
2887
2888 /* Problem 523: NOUN */
2889 integrate(e^(d*z)*(b*%e^(c*z)+a)^p/(e*%e^(c*z)+d),z);
2890 'integrate(e^(d*z)*(b*%e^(c*z)+a)^p/(e*%e^(c*z)+d),z);
2891
2892 /* ----- Involving (a+b*%e^(2*c*z))^p*%e^(c*z) ------------------------------ */
2893
2894 assume(a>0,b>0);
2895 [a>0,b>0];
2896
2897 /* Problem 525: NEW 08-2010 */
2898 integrate((b*%e^(2*c*z)+a)^(5/2)*%e^(c*z),z);
2899 5*a^3*asinh(2*b*%e^(c*z)/sqrt(4*a*b))/(16*sqrt(b)*c)
2900  +%e^(c*z)*(b*%e^(2*c*z)+a)^(5/2)/(6*c)
2901  +5*a*%e^(c*z)*(b*%e^(2*c*z)+a)^(3/2)/(24*c)
2902  +5*a^2*%e^(c*z)*sqrt(b*%e^(2*c*z)+a)/(16*c)$
2903
2904 /* Problem 526: NEW 08-2010 */
2905 integrate((b*%e^(2*c*z)+a)^(3/2)*%e^(c*z),z);
2906 3*a^2*asinh(2*b*%e^(c*z)/sqrt(4*a*b))/(8*sqrt(b)*c)
2907  +%e^(c*z)*(b*%e^(2*c*z)+a)^(3/2)/(4*c)
2908  +3*a*%e^(c*z)*sqrt(b*%e^(2*c*z)+a)/(8*c)$
2909
2910 /* Problem 527: NEW 08-2010 */
2911 integrate((b*%e^(2*c*z)+a)^(1/2)*%e^(c*z),z);
2912 a*asinh(2*b*%e^(c*z)/sqrt(4*a*b))/(2*sqrt(b)*c)
2913  +%e^(c*z)*sqrt(b*%e^(2*c*z)+a)/(2*c)$
2914
2915 /* Problem 528: NEW 08-2010 */
2916 integrate((b*%e^(2*c*z)+a)^((-1)/2)*%e^(c*z),z);
2917 asinh(2*b*%e^(c*z)/sqrt(4*a*b))/(sqrt(b)*c)$
2918
2919 /* Problem 529: NEW 08-2010 */
2920 integrate((b*%e^(2*c*z)+a)^((-3)/2)*%e^(c*z),z);
2921 %e^(c*z)/(a*c*sqrt(b*%e^(2*c*z)+a));
2922
2923 /* Problem 530: NEW 08-2010 */
2924 integrate((b*%e^(2*c*z)+a)^((-5)/2)*%e^(c*z),z);
2925 2*%e^(c*z)/(3*a^2*c*sqrt(b*%e^(2*c*z)+a))
2926  +%e^(c*z)/(3*a*c*(b*%e^(2*c*z)+a)^(3/2));
2927
2928 forget(a>0,b>0);
2929 [a>0,b>0];
2930
2931 /* ----- Involving ((a+b*%e^(2*c*z))^v)^p*%e^(c*z) -------------------------- */
2932
2933 /* Problem 532: NOUN */
2934 integrate(((b*%e^(2*c*z)+a)^v)^p*%e^(c*z),z);
2935 'integrate(%e^(c*z)*((b*%e^(2*c*z)+a)^v)^p,z);
2936
2937 assume(a>0,b>0);
2938 [a>0,b>0];
2939
2940 /* Problem 534: NEW 08-2010 */
2941 integrate(((b*%e^(2*c*z)+a)^5)^(1/2)*%e^(c*z),z),domain:real;
2942 5*a^3*asinh(sqrt(b)*%e^(c*z)/sqrt(a))/(16*sqrt(b)*c)
2943  +%e^(c*z)*(b*%e^(2*c*z)+a)^(5/2)/(6*c)
2944  +5*a*%e^(c*z)*(b*%e^(2*c*z)+a)^(3/2)/(24*c)
2945  +5*a^2*%e^(c*z)*sqrt(b*%e^(2*c*z)+a)/(16*c)$
2946
2947 /* Problem 535: NEW 08-2010 */
2948 integrate(((b*%e^(2*c*z)+a)^3)^(1/2)*%e^(c*z),z),domain:real;
2949 3*a^2*asinh(sqrt(b)*%e^(c*z)/sqrt(a))/(8*sqrt(b)*c)
2950  +%e^(c*z)*(b*%e^(2*c*z)+a)^(3/2)/(4*c)
2951  +3*a*%e^(c*z)*sqrt(b*%e^(2*c*z)+a)/(8*c)$
2952
2953 forget(a>0,b>0);
2954 [a>0,b>0];
2955
2956 /* Problem 537: NEW 08-2010 */
2957 integrate((b*%e^(2*c*z)+a)^(-3/2)*%e^(c*z),z);
2958 %e^(c*z)/(a*c*sqrt(b*%e^(2*c*z)+a));
2959
2960 /* Problem 538: NEW 08-2010 */
2961 integrate((b*%e^(2*c*z)+a)^(-5/2)*%e^(c*z),z);
2962 2*%e^(c*z)/(3*a^2*c*sqrt(b*%e^(2*c*z)+a))
2963  +%e^(c*z)/(3*a*c*(b*%e^(2*c*z)+a)^(3/2));
2964
2965 /* ----- Involving (a+b*%e^(2*c*z))^p*(%e^(c*z))^v -------------------------- */
2966
2967 /* Problem 539: NOUN */
2968 integrate((b*%e^(2*c*z)+a)^p*(%e^(c*z))^v,z);
2969 'integrate((b*%e^(2*c*z)+a)^p*(%e^(c*z))^v,z);
2970
2971 /* Problem 540: NOUN */
2972 integrate((b*%e^(2*c*z)+a)^(5/2)*(%e^(c*z))^v,z);
2973 'integrate((b*%e^(2*c*z)+a)^(5/2)*(%e^(c*z))^v,z);
2974
2975 /* Problem 541: NOUN */
2976 integrate((b*%e^(2*c*z)+a)^(3/2)*(%e^(c*z))^v,z);
2977 'integrate((b*%e^(2*c*z)+a)^(3/2)*(%e^(c*z))^v,z);
2978
2979 /* Problem 542: NOUN */
2980 integrate((b*%e^(2*c*z)+a)^(1/2)*(%e^(c*z))^v,z);
2981 'integrate((b*%e^(2*c*z)+a)^(1/2)*(%e^(c*z))^v,z);
2982
2983 /* Problem 543: NOUN */
2984 integrate((b*%e^(2*c*z)+a)^((-1)/2)*(%e^(c*z))^v,z);
2985 'integrate((b*%e^(2*c*z)+a)^((-1)/2)*(%e^(c*z))^v,z);
2986
2987 /* Problem 544: NOUN */
2988 integrate((b*%e^(2*c*z)+a)^((-3)/2)*(%e^(c*z))^v,z);
2989 'integrate((b*%e^(2*c*z)+a)^((-3)/2)*(%e^(c*z))^v,z);
2990
2991 /* Problem 545: NOUN */
2992 integrate((b*%e^(2*c*z)+a)^((-5)/2)*(%e^(c*z))^v,z);
2993 'integrate((b*%e^(2*c*z)+a)^((-5)/2)*(%e^(c*z))^v,z);
2994
2995 /* ----- Involving %e^(q*z)*(b*%e^(c*z)+a)^p*(e*%e^(c*z)+d)^v --------------- */
2996
2997 /* Problem 546: NOUN */
2998 integrate(%e^(q*z)*(b*%e^(c*z)+a)^p*(e*%e^(c*z)+d)^v,z);
2999 'integrate((b*%e^(c*z)+a)^p*(e*%e^(c*z)+d)^v*%e^(q*z),z);
3000
3001 /* Problem 547: NOUN */
3002 integrate((b*%e^(c*z)+a)^p*(e*%e^(c*z)+d)^v,z);
3003 'integrate((b*%e^(c*z)+a)^p*(e*%e^(c*z)+d)^v,z);
3004
3005 /* ----- Involvoving (a*%e^(2*d*z)+b*%e^(d*z)+c)^p -------------------------- */
3006
3007 /* Problem 548: NOUN */
3008 integrate((c+b*%e^(d*z)+a*%e^(2*d*z))^p,z);
3009 'integrate((a*%e^(2*d*z)+b*%e^(d*z)+c)^p,z);
3010
3011 /* Problem 550: NEW 08-2010
3012  * We get a correct result for x a real variable.
3013  */
3014 assume(a>0,b>0,c>0,4*a*c>b^2);
3015 [a > 0,b > 0,c > 0,4*a*c > b^2];
3016
3017 integrate((c+b*%e^(d*x)+a*%e^(2*d*x))^(1/2),x);
3018 b*asinh((2*a*%e^(d*x)+b)/sqrt(4*a*c-b^2))/(2*sqrt(a)*d)
3019  -sqrt(c)*asinh(2*c*%e^-(d*x)/sqrt(4*a*c-b^2)+b/sqrt(4*a*c-b^2))/d
3020  +sqrt(a*%e^(2*d*x)+b*%e^(d*x)+c)/d;
3021
3022 forget(a>0,b>0,c>0,4*a*c>b^2);
3023 [a > 0,b > 0,c > 0,4*a*c > b^2];
3024
3025 /* ----- Involvoving %e^(e*z)*(a*%e^(2*d*z)+b*%e^(d*z)+c)^p ----------------- */
3026
3027 /* Problem 552: NOUN */
3028 integrate(%e^(e*z)*(c+b*%e^(d*z)+a*%e^(2*d*z))^p,z);
3029 'integrate((a*%e^(2*d*z)+b*%e^(d*z)+c)^p*%e^(e*z),z);
3030
3031 /* ----- Other integrals ---------------------------------------------------- */
3032
3033 assume(a>0,b>0,c>0,d>0);
3034 [a>0,b>0,c>0,d>0];
3035
3036 /* Problem 554: NEW 08-2010 */
3037
3038 integrate(sqrt((b*%e^(e*z)+a)/(d*%e^(e*z)+c)),z);
3039 a*log((2*c*sqrt((b*%e^(e*z)+a)/(d*%e^(e*z)+c))-2*sqrt(a*c))
3040        /(2*c*sqrt((b*%e^(e*z)+a)/(d*%e^(e*z)+c))+2*sqrt(a*c)))
3041  /(sqrt(a*c)*e)
3042  -b*log((2*d*sqrt((b*%e^(e*z)+a)/(d*%e^(e*z)+c))-2*sqrt(b*d))
3043          /(2*d*sqrt((b*%e^(e*z)+a)/(d*%e^(e*z)+c))+2*sqrt(b*d)))
3044   /(sqrt(b*d)*e)$
3045
3046 assume(a*d>b*c);
3047 [a*d>b*c];
3048
3049 /* Problem 556: NEW 08-2010 */
3050 integrate(sqrt((%e^(c*z)-1)/(%e^(c*z)+1)),z);
3051 log(sqrt((%e^(c*z)-1)/(%e^(c*z)+1))+1)/c
3052  -2*atan(sqrt((%e^(c*z)-1)/(%e^(c*z)+1)))/c
3053  -log(sqrt((%e^(c*z)-1)/(%e^(c*z)+1))-1)/c$
3054
3055 forget(a>0,b>0,c>0,d>0,a*d>b*c);
3056 [a>0,b>0,c>0,d>0,a*d>b*c];
3057
3058 /* Problem 558: OK */
3059 integrate(sqrt((%e^(c*z)-1)/(%e^(c*z)+1)),z);
3060 log(sqrt((%e^(c*z)-1)/(%e^(c*z)+1))+1)/c
3061  -2*atan(sqrt((%e^(c*z)-1)/(%e^(c*z)+1)))/c
3062  -log(sqrt((%e^(c*z)-1)/(%e^(c*z)+1))-1)/c;
3063
3064 /* Problem 559: NOUN */
3065 integrate(1/(sqrt(1-%e^z)+sqrt(1+%e^z)),z);
3066 'integrate(1/(sqrt(1-%e^z)+sqrt(1+%e^z)),z);
3067
3068 /* ----- Involving powers of the dircect function and a power function ------ */
3069
3070 /* ----- Involving z^(v-1) and arguments a*z -------------------------------- */
3071
3072 /* Problem 560: NEW 2-1 */
3073 diffcheck(integrate(z^(v-1)*(%e^(a*z))^u,z),z,factor);
3074 z^(v-1)*(%e^(a*z))^u;
3075
3076 /* Problem 561: NEW 2
3077  * We get the most simple result for a real argument x.
3078  */
3079 integrate((%e^(a*x))^u/x,x),gamma_expand:true,logcontract;
3080 expintegral_ei(a*u*x);
3081
3082 /* Problem 562: NEW 2-1 */
3083 diffcheck(integrate(z^n*(%e^(a*z))^u,z),z,factor);
3084 z^n*(%e^(a*z))^u;
3085
3086 /* Problem 563: OK */
3087 integrate(z*(%e^(a*z))^u,z), domain:real;
3088 (a*u*z-1)*%e^(a*u*z)/(a^2*u^2);
3089
3090 /* Problem 564: NEW 2-1*/
3091 integrate(z^(1/2+n)*(%e^(a*z))^u,z);
3092 -gamma_incomplete(n+3/2,-a*u*z)*z^(n+3/2)*(-a*u*z)^(-n-3/2)*(%e^(a*z))^u
3093                                *%e^-(a*u*z);
3094
3095 /* ----- Involving z^(v-1) and arguments a*z+b ------------------------------ */
3096
3097 /* Problem 565: NEW 2-1 */
3098 -integrate(z^(v-1)*(%e^(a*z+b))^u,z);
3099 gamma_incomplete(v,-a*u*z)*z^v*%e^-(a*u*z)*(%e^(a*z+b))^u/(-a*u*z)^v;
3100
3101 /* Problem 566: NEW Typ 2
3102  * We get the most simple result only for a real argument x.
3103  */
3104 integrate((%e^(a*x+b))^u/x,x),gamma_expand:true,logcontract;
3105 %e^(b*u)*expintegral_ei(a*u*x);
3106
3107 /* Problem 567: NEW 2-1 */
3108 integrate(z^n*(%e^(a*z+b))^u,z);
3109 -a^(-n-1)*(-1)^(n+1)*gamma_incomplete(n+1,-a*u*z)*u^(-n-1)*%e^-(a*u*z)
3110          *(%e^(a*z+b))^u;
3111
3112 /* Problem 568: OK */
3113 integrate(z*(%e^(a*z+b))^u,z), domain:real;
3114 (a*u*%e^(b*u)*z-%e^(b*u))*%e^(a*u*z)/(a^2*u^2);
3115
3116 /* Problem 569: NEW 2-1 */
3117 -integrate(z^(1/2+n)*(%e^(a*z+b))^u,z);
3118 gamma_incomplete(n+3/2,-a*u*z)*z^(n+3/2)*(-a*u*z)^(-n-3/2)*%e^-(a*u*z)
3119                               *(%e^(a*z+b))^u;
3120
3121 /* ----- Involving z^(v-1) and arguments a*z^r ------------------------------ */
3122
3123 /* Problem 570: NEW 2-1 */
3124 integrate(z^(v-1)*(%e^(a*z^r))^u,z);
3125 -gamma_incomplete(v/r,-a*u*z^r)*z^v*(%e^(a*z^r))^u*%e^-(a*u*z^r)
3126  /(r*(-a*u*z^r)^(v/r));
3127
3128 /* Problem 571: NEW 2
3129  * We get the most simple result only for a real argument x.
3130  */
3131 integrate((%e^(a*x^r))^u/x,x),gamma_expand:true,logcontract;
3132 expintegral_ei(a*u*x^r)/r;
3133
3134 /* Problem 572: NEW 2-1 */
3135 integrate(z^n*(%e^(a*z^2))^u,z);
3136 -gamma_incomplete((n+1)/2,-a*u*z^2)*z^(n+1)*(-a*u*z^2)^((-n-1)/2)
3137                                    *(%e^(a*z^2))^u*%e^-(a*u*z^2)
3138  /2;
3139
3140 /* Problem 573: NEW 2-1 */
3141 integrate(z^(2*n)*(%e^(a*z^2))^u,z);
3142 -gamma_incomplete((2*n+1)/2,-a*u*z^2)*z^(2*n+1)*(-a*u*z^2)^((-2*n-1)/2)
3143                                      *(%e^(a*z^2))^u*%e^-(a*u*z^2)
3144  /2;
3145
3146 /* Problem 574: NEW 2-1 */
3147 integrate(z^(1+2*n)*(%e^(a*z^2))^u,z),factor;
3148 a^(-n-1)*(-1)^n*gamma_incomplete(n+1,-a*u*z^2)*u^(-n-1)*(%e^(a*z^2))^u
3149         *%e^-(a*u*z^2)
3150  /2;
3151
3152 /* Problem 575: NEW 2-1 */
3153 integrate(z^n*(%e^(a*sqrt(z)))^u,z),factor;
3154 -2*a^(-2*n-2)*gamma_incomplete(2*(n+1),-a*u*sqrt(z))*u^(-2*n-2)
3155   *(%e^(a*sqrt(z)))^u*%e^-(a*u*sqrt(z));
3156
3157 /* ----- Involving z^(v-1) and arguments a*z^r+b ---------------------------- */
3158
3159 /* Problem 576: NEW 2-1*/
3160 integrate(z^(v-1)*(%e^(b+a*z^r))^u,z);
3161 -gamma_incomplete(v/r,-a*u*z^r)*z^v*%e^-(a*u*z^r)*(%e^(a*z^r+b))^u
3162  /(r*(-a*u*z^r)^(v/r));
3163
3164 /* Problem 577: NEW 2
3165  * We get the most simple result only for a real argument x.
3166  */
3167 integrate((%e^(b+a*x^r))^u/x,x),gamma_expand:true,logcontract;
3168 %e^(b*u)*expintegral_ei(a*u*x^r)/r;
3169
3170 /* Problem 578: NEW 2-1 */
3171 integrate(z^n*(%e^(b+a*z^2))^u,z),ratsimp;
3172 -gamma_incomplete((n+1)/2,-a*u*z^2)*z^(n+1)*(-a*u*z^2)^(-n/2-1/2)
3173                                    *%e^-(a*u*z^2)*(%e^(a*z^2+b))^u
3174  /2;
3175
3176 /* Problem 579: NEW 2-1 */
3177 integrate(z^(2*n)*(%e^(b+a*z^2))^u,z),ratsimp;
3178 -(-1)^n*gamma_incomplete((2*n+1)/2,-a*u*z^2)*z*%e^-(a*u*z^2)*(%e^(a*z^2+b))^u
3179  /(2*a^n*u^n*sqrt(-a*u*z^2));
3180
3181 /* Problem 580: NEW 2-1 */
3182 integrate(z^(1+2*n)*(%e^(b+a*z^2))^u,z),ratsimp;
3183 a^(-n-1)*(-1)^n*gamma_incomplete(n+1,-a*u*z^2)*u^(-n-1)*%e^-(a*u*z^2)
3184         *(%e^(a*z^2+b))^u
3185  /2;
3186
3187 /* Problem 581: NEW 2-1 */
3188 integrate(z^n*(%e^(b+a*sqrt(z)))^u,z),ratsimp;
3189 -2*a^(-2*n-2)*gamma_incomplete(2*n+2,-a*u*sqrt(z))*u^(-2*n-2)
3190   *%e^-(a*u*sqrt(z))*(%e^(a*sqrt(z)+b))^u;
3191
3192 /* ----- Involving z^(v-1) and arguments a*z^r+b*z -------------------------- */
3193
3194 /* Problem 582: NEW 5-1 */
3195 expand(niceindices(integrate(z^n*(%e^(b*z+a*z^2))^u,z))-
3196 (-a^(-n-1)*(%e^(a*z^2+b*z))^u*%e^(-u*(a*z^2+b*z)-b^2*u/(4*a))
3197          *('sum(b^(n-i)*gamma_incomplete((i+1)/2,-u*(2*a*z+b)^2/(4*a))
3198                        *(-1)^(i-n)*2^(i-n)*binomial(n,i)*(2*a*z+b)^(i+1)
3199                  /(-u*(2*a*z+b)^2/a)^((i+1)/2),i,0,n))
3200  /2));
3201 0;
3202
3203 /* Problem 583: NEW 6-1 */
3204 niceindices(integrate(z^n*(%e^(b*z+a*sqrt(z)))^u,z));
3205 2^(-2*n-1)*('sum(4^j*binomial(n,j)
3206                     *'sum(a^(2*n-j-i)*(-1)^(i-j)*binomial(j,i)
3207                                      *(2*b*sqrt(z)+a)^(j+i)
3208                                      *(a
3209                                       *gamma_incomplete((j+i+1)/2,
3210                                                         -u*(2*b*sqrt(z)+a)^2
3211                                                          /(4*b))
3212                                       *(2*b*sqrt(z)+a)
3213                                       +2*b
3214                                         *gamma_incomplete((j+i+2)/2,
3215                                                           -u*(2*b*sqrt(z)+a)^2
3216                                                            /(4*b))
3217                                         *sqrt(-u*(2*b*sqrt(z)+a)^2/b)
3218                                        /u)
3219                            /(-u*(2*b*sqrt(z)+a)^2/b)^((j+i+1)/2),i,0,j),j,0,
3220                  n))*(%e^(b*z+a*sqrt(z)))^u*%e^(u*(b*z+a*sqrt(z))-a^2*u/(4*b))
3221  /b^(2*(n+1));
3222
3223 /* ----- Involving z^(v-1) and arguments a*z^r+b*z+c ------------------------ */
3224
3225 /* Problem 584: NEW 5-1 */
3226 expand(niceindices(integrate(z^n*(%e^(c+b*z+a*z^2))^u,z))-
3227 (-a^(-n-1)*(%e^(a*z^2+b*z+c))^u*%e^(-u*(a*z^2+b*z)-b^2*u/(4*a))
3228          *('sum(b^(n-i)*gamma_incomplete((i+1)/2,-u*(2*a*z+b)^2/(4*a))
3229                        *(-1)^(i-n)*2^(i-n)*binomial(n,i)*(2*a*z+b)^(i+1)
3230                  /(-u*(2*a*z+b)^2/a)^((i+1)/2),i,0,n))
3231  /2));
3232 0;
3233
3234 /* Problem 585: NEW 6-1 */
3235 niceindices(integrate(z^n*(%e^(c+b*z+a*sqrt(z)))^u,z));
3236 2^(-2*n-1)*('sum(4^j*binomial(n,j)
3237                     *'sum(a^(2*n-j-i)*(-1)^(i-j)*binomial(j,i)
3238                                      *(2*b*sqrt(z)+a)^(j+i)
3239                                      *(a
3240                                       *gamma_incomplete((j+i+1)/2,
3241                                                         -u*(2*b*sqrt(z)+a)^2
3242                                                          /(4*b))
3243                                       *(2*b*sqrt(z)+a)
3244                                       +2*b
3245                                         *gamma_incomplete((j+i+2)/2,
3246                                                           -u*(2*b*sqrt(z)+a)^2
3247                                                            /(4*b))
3248                                         *sqrt(-u*(2*b*sqrt(z)+a)^2/b)
3249                                        /u)
3250                            /(-u*(2*b*sqrt(z)+a)^2/b)^((j+i+1)/2),i,0,j),j,0,
3251                  n))*(%e^(b*z+a*sqrt(z)))^u
3252           *%e^(u*(b*z+a*sqrt(z)+c)-a^2*u/(4*b))
3253  /b^(2*(n+1));
3254
3255 /* ----- Involving z^(v-1)*a^(d*z)*h^(c*z) ---------------------------------- */
3256
3257 /* Problem 586: NEW 7 */
3258 expand(integrate(z^(v-1)*a^(d*z)*h^(c*z),z)-
3259 (-gamma_incomplete(v,-(c*log(h)+log(a)*d)*z)*z^v/(-(c*log(h)+log(a)*d)*z)^v));
3260 0;
3261
3262 /* Problem 587: NEW 7 */
3263 expand(integrate(z^n*a^(d*z)*h^(c*z),z) -
3264 (-(c*log(h)+log(a)*d)^(-n-1)*(-1)^(n+1)
3265                            *gamma_incomplete(n+1,-(c*log(h)+log(a)*d)*z)));
3266 0;
3267
3268 /* Problem 588: NEW 7 */
3269 expand(integrate(z^(1/2+n)*a^(d*z)*h^(c*z),z)-
3270 (-gamma_incomplete(n+3/2,-(c*log(h)+log(a)*d)*z)
3271  *z^(n+3/2)*(-(c*log(h)+log(a)*d)*z)^(-n-3/2)));
3272 0;
3273
3274 /* ----- Involving z^(v-1)*a^(d*z)*h^(c*z+g) -------------------------------- */
3275
3276 /* Problem 589: NEW 7 */
3277 expand(integrate(z^(v-1)*a^(d*z)*h^(g+c*z),z)-
3278 -h^g*gamma_incomplete(v,-(c*log(h)+log(a)*d)*z)*z^v/(-(c*log(h)+log(a)*d)*z)^v);
3279 0;
3280
3281 /* Problem 590: NEW 7 */
3282 expand(integrate(z^n*a^(d*z)*h^(g+c*z),z)-
3283 -h^g*(c*log(h)+log(a)*d)^(-n-1)*(-1)^(n+1)
3284     *gamma_incomplete(n+1,-(c*log(h)+log(a)*d)*z));
3285 0;
3286
3287 /* Problem 591: NEW 7 */
3288 expand(integrate(z^(1/2+n)*a^(d*z)*h^(g+c*z),z)-
3289 -h^g*gamma_incomplete(n+3/2,-(c*log(h)+log(a)*d)*z)*z^(n+3/2)
3290     *(-(c*log(h)+log(a)*d)*z)^(-n-3/2));
3291 0;
3292
3293 /* ----- Involving z^(v-1)*a^(d*z+e)*h^(c*z+g) ------------------------------ */
3294
3295 /* Problem 592: NEW 7 */
3296 expand(integrate(z^(v-1)*a^(e+d*z)*h^(g+c*z),z)-
3297 -a^e*h^g*gamma_incomplete(v,-(c*log(h)+log(a)*d)*z)*z^v
3298  /(-(c*log(h)+log(a)*d)*z)^v);
3299 0;
3300
3301 /* Problem 593: NEW 7 */
3302 expand(integrate(z^n*a^(e+d*z)*h^(g+c*z),z)-
3303 -a^e*h^g*(c*log(h)+log(a)*d)^(-n-1)*(-1)^(n+1)
3304     *gamma_incomplete(n+1,-(c*log(h)+log(a)*d)*z));
3305 0;
3306
3307 /* Problem 594: NEW 7 */
3308 expand(integrate(z^(1/2+n)*a^(e+d*z)*h^(g+c*z),z)-
3309 -a^e*h^g*gamma_incomplete(n+3/2,-(c*log(h)+log(a)*d)*z)*z^(n+3/2)
3310     *(-(c*log(h)+log(a)*d)*z)^(-n-3/2));
3311 0;
3312
3313 /* ----- Involving z^n*a^(b*z)*h^(c*z^r) ------------------------------------ */
3314
3315 /* Problem 595: NEW 9 */
3316 expand(niceindices(integrate(z^n*a^(b*z)*h^(c*z^2),z))-
3317 (-c^(-n-1)*%e^-(log(a)^2*b^2/(4*c*log(h)))*log(h)^(-n-1)
3318          *('sum(log(a)^(n-i)*b^(n-i)
3319                             *gamma_incomplete((i+1)/2,
3320                                               -(2*c*log(h)*z+log(a)*b)^2
3321                                                /(4*c*log(h)))*(-1)^(i-n)
3322                             *2^(i-n)*binomial(n,i)
3323                             *(2*c*log(h)*z+log(a)*b)^(i+1)
3324                  /(-(2*c*log(h)*z+log(a)*b)^2/(c*log(h)))^((i+1)/2),i,0,n))
3325  /2));
3326 0;
3327
3328 /* Problem 596: NEW 10 */
3329 expand(niceindices(integrate(z^n*a^(b*z)*h^(c*sqrt(z)),z))-
3330 (%e^-(c^2*log(h)^2/(4*log(a)*b))*2^(-2*n-1)
3331                                *('sum(4^j*binomial(n,j)
3332                                          *'sum(
3333                                           c^(2*n-j-i)*log(h)^(2*n-j-i)
3334                                                      *(-1)^(i-j)*binomial(j,i)
3335                                                      *(2*log(a)*b*sqrt(z)
3336                                                       +c*log(h))
3337                                                       ^(j+i)
3338                                                      *(c*log(h)
3339                                                         *gamma_incomplete(
3340                                                          (j+i+1)/2,
3341                                                          -(2*log(a)*b*sqrt(z)
3342                                                           +c*log(h))
3343                                                           ^2
3344                                                           /(4*log(a)*b))
3345                                                         *(2*log(a)*b*sqrt(z)
3346                                                          +c*log(h))
3347                                                       +2*log(a)*b
3348                                                         *gamma_incomplete(
3349                                                          (j+i+2)/2,
3350                                                          -(2*log(a)*b*sqrt(z)
3351                                                           +c*log(h))
3352                                                           ^2
3353                                                           /(4*log(a)*b))
3354                                                         *sqrt(
3355                                                          -(2*log(a)*b*sqrt(z)
3356                                                           +c*log(h))
3357                                                           ^2
3358                                                           /(log(a)*b)))
3359                                            /(-(2*log(a)*b*sqrt(z)+c*log(h))^2
3360                                             /(log(a)*b))
3361                                             ^((j+i+1)/2),i,0,j),j,0,n))
3362  /(log(a)^(2*(n+1))*b^(2*(n+1)))));
3363 0;
3364
3365 /* ----- Involving z^n*a^(d*z+e)*h^(c*z^r) ---------------------------------- */
3366
3367 /* Problem 597: NEW 9 */
3368 expand(niceindices(integrate(z^n*a^(e+d*z)*h^(c*z^2),z))-
3369 (-a^e*c^(-n-1)*%e^-(log(a)^2*d^2/(4*c*log(h)))*log(h)^(-n-1)
3370     *('sum(log(a)^(n-i)*d^(n-i)
3371                        *gamma_incomplete((i+1)/2,
3372                                          -(2*c*log(h)*z+log(a)*d)^2
3373                                           /(4*c*log(h)))*(-1)^(i-n)*2^(i-n)
3374                        *binomial(n,i)*(2*c*log(h)*z+log(a)*d)^(i+1)
3375             /(-(2*c*log(h)*z+log(a)*d)^2/(c*log(h)))^((i+1)/2),i,0,n))
3376  /2));
3377 0;
3378
3379 /* Problem 598: NEW 10 */
3380 expand(niceindices(integrate(z^n*a^(e+d*z)*h^(c*sqrt(z)),z))-
3381 (a^e*%e^-(c^2*log(h)^2/(4*log(a)*d))*2^(-2*n-1)
3382    *('sum(4^j*binomial(n,j)
3383              *'sum(c^(2*n-j-i)*log(h)^(2*n-j-i)*(-1)^(i-j)*binomial(j,i)
3384                               *(2*log(a)*d*sqrt(z)+c*log(h))^(j+i)
3385                               *(c*log(h)
3386                                  *gamma_incomplete((j+i+1)/2,
3387                                                    -(2*log(a)*d*sqrt(z)
3388                                                     +c*log(h))
3389                                                     ^2
3390                                                     /(4*log(a)*d))
3391                                  *(2*log(a)*d*sqrt(z)+c*log(h))
3392                                +2*log(a)*d
3393                                  *gamma_incomplete((j+i+2)/2,
3394                                                    -(2*log(a)*d*sqrt(z)
3395                                                     +c*log(h))
3396                                                     ^2
3397                                                     /(4*log(a)*d))
3398                                  *sqrt(-(2*log(a)*d*sqrt(z)+c*log(h))^2
3399                                         /(log(a)*d)))
3400                     /(-(2*log(a)*d*sqrt(z)+c*log(h))^2/(log(a)*d))
3401                      ^((j+i+1)/2),i,0,j),j,0,n))
3402  /(log(a)^(2*(n+1))*d^(2*(n+1)))));
3403 0;
3404
3405 /* ----- Involving z^(v-1)*a^(b*z^r)*h^(c*z^r) ------------------------------ */
3406
3407 /* Problem 599: NEW 7 */
3408 expand(integrate(z^(v-1)*a^(b*z^r)*h^(c*z^r),z)-
3409 -gamma_incomplete(v/r,-(c*log(h)+log(a)*b)*z^r)*z^v
3410  /(r*(-(c*log(h)+log(a)*b)*z^r)^(v/r)));
3411 0;
3412
3413 /* Problem 600: NEW 7 */
3414 expand(integrate(z^n*a^(b*z^2)*h^(c*z^2),z)-
3415 (-gamma_incomplete((n+1)/2,-(c*log(h)+log(a)*b)*z^2)
3416  *z^(n+1)*(-(c*log(h)+log(a)*b)*z^2)^((-n-1)/2)
3417  /2));
3418 0;
3419
3420 /* Problem 601: NEW 7 */
3421 expand(integrate(z^(2*n)*a^(b*z^2)*h^(c*z^2),z)-
3422 (-gamma_incomplete((2*n+1)/2,-(c*log(h)+log(a)*b)*z^2)
3423  *z^(2*n+1)*(-(c*log(h)+log(a)*b)*z^2)^((-2*n-1)/2)
3424  /2));
3425 0;
3426
3427 /* Problem 602: NEW 7 */
3428 expand(integrate(z^(1+2*n)*a^(b*z^2)*h^(c*z^2),z)-
3429 -(c*log(h)+log(a)*b)^((-2*n-2)/2)*(-1)^((-2*n-2)/2)
3430                                  *gamma_incomplete((2*n+2)/2,
3431                                                    -(c*log(h)+log(a)*b)*z^2)
3432  /2);
3433 0;
3434
3435 /* Problem 603: NEW 7 */
3436 expand(integrate(z^n*a^(b*sqrt(z))*h^(c*sqrt(z)),z)-
3437 (-2*(c*log(h)+log(a)*b)^(2*(-n-1))
3438   *gamma_incomplete(2*(n+1),-(c*log(h)+log(a)*b)*sqrt(z))));
3439 0;
3440
3441 /* ----- Involving z^n*a^(d*z)*h^(c*z^r+g) ---------------------------------- */
3442
3443 /* Problem 604: NEW 9 */
3444 expand(niceindices(integrate(z^n*a^(d*z)*h^(g+c*z^2),z))-
3445 (-c^(-n-1)*h^g*%e^-(log(a)^2*d^2/(4*c*log(h)))*log(h)^(-n-1)
3446          *('sum(log(a)^(n-i)*d^(n-i)
3447                             *gamma_incomplete((i+1)/2,
3448                                               -(2*c*log(h)*z+log(a)*d)^2
3449                                                /(4*c*log(h)))*(-1)^(i-n)
3450                             *2^(i-n)*binomial(n,i)
3451                             *(2*c*log(h)*z+log(a)*d)^(i+1)
3452                  /(-(2*c*log(h)*z+log(a)*d)^2/(c*log(h)))^((i+1)/2),i,0,n))
3453  /2));
3454 0;
3455
3456 /* Problem 605: NEW 10 */
3457 expand(niceindices(integrate(z^n*a^(d*z)*h^(g+c*sqrt(z)),z))-
3458 (h^g*%e^-(c^2*log(h)^2/(4*log(a)*d))*2^(-2*n-1)
3459    *('sum(4^j*binomial(n,j)
3460              *'sum(c^(2*n-j-i)*log(h)^(2*n-j-i)*(-1)^(i-j)*binomial(j,i)
3461                               *(2*log(a)*d*sqrt(z)+c*log(h))^(j+i)
3462                               *(c*log(h)
3463                                  *gamma_incomplete((j+i+1)/2,
3464                                                    -(2*log(a)*d*sqrt(z)
3465                                                     +c*log(h))
3466                                                     ^2
3467                                                     /(4*log(a)*d))
3468                                  *(2*log(a)*d*sqrt(z)+c*log(h))
3469                                +2*log(a)*d
3470                                  *gamma_incomplete((j+i+2)/2,
3471                                                    -(2*log(a)*d*sqrt(z)
3472                                                     +c*log(h))
3473                                                     ^2
3474                                                     /(4*log(a)*d))
3475                                  *sqrt(-(2*log(a)*d*sqrt(z)+c*log(h))^2
3476                                         /(log(a)*d)))
3477                     /(-(2*log(a)*d*sqrt(z)+c*log(h))^2/(log(a)*d))
3478                      ^((j+i+1)/2),i,0,j),j,0,n))
3479  /(log(a)^(2*(n+1))*d^(2*(n+1)))));
3480 0;
3481
3482 /* ----- Involving z^n*a^(d*z+e)*h^(c*z^r+g) -------------------------------- */
3483
3484 /* Problem 606: NEW 9 */
3485 expand(niceindices(integrate(z^n*a^(e+d*z)*h^(g+c*z^2),z))-
3486 (-a^e*c^(-n-1)*h^g*%e^-(log(a)^2*d^2/(4*c*log(h)))*log(h)^(-n-1)
3487     *('sum(log(a)^(n-i)*d^(n-i)
3488                        *gamma_incomplete((i+1)/2,
3489                                          -(2*c*log(h)*z+log(a)*d)^2
3490                                           /(4*c*log(h)))*(-1)^(i-n)*2^(i-n)
3491                        *binomial(n,i)*(2*c*log(h)*z+log(a)*d)^(i+1)
3492             /(-(2*c*log(h)*z+log(a)*d)^2/(c*log(h)))^((i+1)/2),i,0,n))
3493  /2));
3494 0;
3495
3496 /* Problem 607: NEW 10 */
3497 expand(niceindices(integrate(z^n*a^(e+d*z)*h^(g+c*sqrt(z)),z))-
3498 (a^e*h^g*%e^-(c^2*log(h)^2/(4*log(a)*d))*2^(-2*n-1)
3499    *('sum(4^j*binomial(n,j)
3500              *'sum(c^(2*n-j-i)*log(h)^(2*n-j-i)*(-1)^(i-j)*binomial(j,i)
3501                               *(2*log(a)*d*sqrt(z)+c*log(h))^(j+i)
3502                               *(c*log(h)
3503                                  *gamma_incomplete((j+i+1)/2,
3504                                                    -(2*log(a)*d*sqrt(z)
3505                                                     +c*log(h))
3506                                                     ^2
3507                                                     /(4*log(a)*d))
3508                                  *(2*log(a)*d*sqrt(z)+c*log(h))
3509                                +2*log(a)*d
3510                                  *gamma_incomplete((j+i+2)/2,
3511                                                    -(2*log(a)*d*sqrt(z)
3512                                                     +c*log(h))
3513                                                     ^2
3514                                                     /(4*log(a)*d))
3515                                  *sqrt(-(2*log(a)*d*sqrt(z)+c*log(h))^2
3516                                         /(log(a)*d)))
3517                     /(-(2*log(a)*d*sqrt(z)+c*log(h))^2/(log(a)*d))
3518                      ^((j+i+1)/2),i,0,j),j,0,n))
3519  /(log(a)^(2*(n+1))*d^(2*(n+1)))));
3520 0;
3521
3522 /* ----- Involving z^(v-1)*a^(b*z^r)*h^(c*z^r+g) ---------------------------- */
3523
3524 /* Problem 608: NEW 7 */
3525 expand(integrate(z^(v-1)*a^(b*z^r)*h^(g+c*z^r),z)-
3526 -h^g*gamma_incomplete(v/r,-(c*log(h)+log(a)*b)*z^r)*z^v
3527  /(r*(-(c*log(h)+log(a)*b)*z^r)^(v/r)));
3528 0;
3529
3530 /* Problem 609: NEW 7 */
3531 expand(integrate(z^n*a^(b*z^2)*h^(g+c*z^2),z)-
3532 (-h^g*gamma_incomplete((n+1)/2,-(c*log(h)+log(a)*b)*z^2)*z^(n+1)
3533     *(-(c*log(h)+log(a)*b)*z^2)^((-n-1)/2)
3534  /2));
3535 0;
3536
3537 /* Problem 610: NEW 7 */
3538 expand(integrate(z^(2*n)*a^(b*z^2)*h^(g+c*z^2),z)-
3539 (-h^g*gamma_incomplete((2*n+1)/2,-(c*log(h)+log(a)*b)*z^2)*z^(2*n+1)
3540     *(-(c*log(h)+log(a)*b)*z^2)^((-2*n-1)/2)
3541  /2));
3542 0;
3543
3544 /* Problem 611: NEW 7 */
3545 expand(integrate(z^(1+2*n)*a^(b*z^2)*h^(g+c*z^2),z)-
3546 -h^g*(c*log(h)+log(a)*b)^((-2*n-2)/2)*(-1)^((-2*n-2)/2)
3547     *gamma_incomplete((2*n+2)/2,-(c*log(h)+log(a)*b)*z^2)
3548  /2);
3549 0;
3550
3551 /* Problem 612: NEW 7 */
3552 expand(integrate(z^(1+2*n)*a^(b*sqrt(z))*h^(g+c*sqrt(z)),z)-
3553 -2*h^g*(c*log(h)+log(a)*b)^(2*(-2*n-2))
3554   *gamma_incomplete(2*(2*n+2),-(c*log(h)+log(a)*b)*sqrt(z)));
3555 0;
3556
3557 /* ----- Involving z^(v-1)*a^(b*z^r+e)*h^(c*z^r+g) -------------------------- */
3558
3559 /* Problem 613: NEW 7 */
3560 expand(integrate(z^(v-1)*a^(e+b*z^r)*h^(g+c*z^r),z)-
3561 -a^e*h^g*gamma_incomplete(v/r,-(c*log(h)+log(a)*b)*z^r)*z^v
3562  /(r*(-(c*log(h)+log(a)*b)*z^r)^(v/r)));
3563 0;
3564
3565 /* Problem 614: NEW 7 */
3566 expand(integrate(z^n*a^(e+b*z^2)*h^(g+c*z^2),z)-
3567 (-a^e*h^g*gamma_incomplete((n+1)/2,-(c*log(h)+log(a)*b)*z^2)*z^(n+1)
3568     *(-(c*log(h)+log(a)*b)*z^2)^((-n-1)/2)
3569  /2));
3570 0;
3571
3572 /* Problem 615: NEW 7 */
3573 expand(integrate(z^(2*n)*a^(e+b*z^2)*h^(g+c*z^2),z)-
3574 (-a^e*h^g*gamma_incomplete((2*n+1)/2,-(c*log(h)+log(a)*b)*z^2)*z^(2*n+1)
3575     *(-(c*log(h)+log(a)*b)*z^2)^((-2*n-1)/2)
3576  /2));
3577 0;
3578
3579 /* Problem 616: NEW 7 */
3580 expand(integrate(z^(1+2*n)*a^(e+b*z^2)*h^(g+c*z^2),z)-
3581 -a^e*h^g*(c*log(h)+log(a)*b)^((-2*n-2)/2)*(-1)^((-2*n-2)/2)
3582     *gamma_incomplete((2*n+2)/2,-(c*log(h)+log(a)*b)*z^2)
3583  /2);
3584 0;
3585
3586 /* Problem 617: NEW 7 */
3587 expand(integrate(z^(1+2*n)*a^(e+b*sqrt(z))*h^(g+c*sqrt(z)),z)-
3588 -2*a^e*h^g*(c*log(h)+log(a)*b)^(2*(-2*n-2))
3589   *gamma_incomplete(2*(2*n+2),-(c*log(h)+log(a)*b)*sqrt(z)));
3590 0;
3591
3592 /* ----- Involving z^n*a^(d*z)*h^(c*z^r+f*z) -------------------------------- */
3593
3594 /* Problem 618: NEW 9 */
3595 expand(niceindices(integrate(z^n*a^(d*z)*h^(f*z+c*z^2),z))-
3596 (-c^(-n-1)*%e^-((f*log(h)+log(a)*d)^2/(4*c*log(h)))*log(h)^(-n-1)
3597          *('sum((-f*log(h)-log(a)*d)^(n-i)
3598                  *gamma_incomplete((i+1)/2,
3599                                    -(log(h)*(2*c*z+f)+log(a)*d)^2
3600                                     /(4*c*log(h)))*2^(i-n)*binomial(n,i)
3601                  *(log(h)*(2*c*z+f)+log(a)*d)^(i+1)
3602                  /(-(log(h)*(2*c*z+f)+log(a)*d)^2/(c*log(h)))^((i+1)/2),i,0,
3603                 n))
3604  /2));
3605 0;
3606
3607 /* Problem 619: NEW 10 */
3608 expand(niceindices(integrate(z^n*a^(d*z)*h^(f*z+c*sqrt(z)),z)) -
3609 (%e^-(c^2*log(h)^2/(4*(f*log(h)+log(a)*d)))
3610  *2^(-2*n-1)
3611  *('sum(4^j*binomial(n,j)
3612            *'sum(c^(2*n-j-i)*log(h)^(2*n-j-i)*(-1)^(i-j)*binomial(j,i)
3613                             *(2*(f*log(h)+log(a)*d)*sqrt(z)+c*log(h))^(j+i)
3614                             *(c*log(h)
3615                                *gamma_incomplete((j+i+1)/2,
3616                                                  -(2*(f*log(h)+log(a)*d)
3617                                                     *sqrt(z)
3618                                                   +c*log(h))
3619                                                   ^2
3620                                                   /(4*(f*log(h)+log(a)*d)))
3621                                *(2*(f*log(h)+log(a)*d)*sqrt(z)+c*log(h))
3622                              +2*(f*log(h)+log(a)*d)
3623                                *gamma_incomplete((j+i+2)/2,
3624                                                  -(2*(f*log(h)+log(a)*d)
3625                                                     *sqrt(z)
3626                                                   +c*log(h))
3627                                                   ^2
3628                                                   /(4*(f*log(h)+log(a)*d)))
3629                                *sqrt(-(2*(f*log(h)+log(a)*d)*sqrt(z)+c*log(h))
3630                                       ^2
3631                                       /(f*log(h)+log(a)*d)))
3632                   /(-(2*(f*log(h)+log(a)*d)*sqrt(z)+c*log(h))^2
3633                    /(f*log(h)+log(a)*d))
3634                    ^((j+i+1)/2),i,0,j),j,0,n))
3635  /(f*log(h)+log(a)*d)^(2*(n+1))));
3636 0;
3637
3638 /* ----- Involving z^n*a^(d*z+e)*h^(c*z^r+f*z) ------------------------------ */
3639
3640 /* Problem 620: NEW 9 */
3641 expand(niceindices(integrate(z^n*a^(e+d*z)*h^(f*z+c*z^2),z))-
3642 (-a^e*c^(-n-1)*%e^-((f*log(h)+log(a)*d)^2/(4*c*log(h)))*log(h)^(-n-1)
3643     *('sum((-f*log(h)-log(a)*d)^(n-i)*gamma_incomplete((i+1)/2,
3644                                                        -(log(h)*(2*c*z+f)
3645                                                         +log(a)*d)
3646                                                         ^2
3647                                                         /(4*c*log(h)))*2^(i-n)
3648                                      *binomial(n,i)
3649                                      *(log(h)*(2*c*z+f)+log(a)*d)^(i+1)
3650             /(-(log(h)*(2*c*z+f)+log(a)*d)^2/(c*log(h)))^((i+1)/2),i,0,n))
3651  /2));
3652 0;
3653
3654 /* Problem 621: NEW 10 */
3655 expand(niceindices(integrate(z^n*a^(e+d*z)*h^(f*z+c*sqrt(z)),z))-
3656 (a^e*%e^-(c^2*log(h)^2/(4*(f*log(h)+log(a)*d)))*2^(-2*n-1)
3657    *('sum(4^j*binomial(n,j)
3658              *'sum(c^(2*n-j-i)*log(h)^(2*n-j-i)*(-1)^(i-j)*binomial(j,i)
3659                               *(2*(f*log(h)+log(a)*d)*sqrt(z)+c*log(h))^(j+i)
3660                               *(c*log(h)
3661                                  *gamma_incomplete((j+i+1)/2,
3662                                                    -(2*(f*log(h)+log(a)*d)
3663                                                       *sqrt(z)
3664                                                     +c*log(h))
3665                                                     ^2
3666                                                     /(4*(f*log(h)+log(a)*d)))
3667                                  *(2*(f*log(h)+log(a)*d)*sqrt(z)+c*log(h))
3668                                +2*(f*log(h)+log(a)*d)
3669                                  *gamma_incomplete((j+i+2)/2,
3670                                                    -(2*(f*log(h)+log(a)*d)
3671                                                       *sqrt(z)
3672                                                     +c*log(h))
3673                                                     ^2
3674                                                     /(4*(f*log(h)+log(a)*d)))
3675                                  *sqrt(-(2*(f*log(h)+log(a)*d)*sqrt(z)
3676                                         +c*log(h))
3677                                         ^2
3678                                         /(f*log(h)+log(a)*d)))
3679                     /(-(2*(f*log(h)+log(a)*d)*sqrt(z)+c*log(h))^2
3680                      /(f*log(h)+log(a)*d))
3681                      ^((j+i+1)/2),i,0,j),j,0,n))
3682  /(f*log(h)+log(a)*d)^(2*(n+1))));
3683 0;
3684
3685 /* ----- Involving z^n*a^(b*z^r)*h^(c*z^r+f*z) ------------------------------ */
3686
3687 /* Problem 622: NEW 9 */
3688 expand(niceindices(integrate(z^n*a^(b*z^2)*h^(f*z+c*z^2),z))-
3689 (-%e^-(f^2*log(h)^2/(4*(c*log(h)+log(a)*b)))
3690  *(c*log(h)+log(a)*b)^(-n-1)
3691  *('sum(f^(n-i)*log(h)^(n-i)
3692                *gamma_incomplete((i+1)/2,
3693                                  -(log(h)*(2*c*z+f)+2*log(a)*b*z)^2
3694                                   /(4*(c*log(h)+log(a)*b)))*(-1)^(i-n)*2^(i-n)
3695                *binomial(n,i)*(log(h)*(2*c*z+f)+2*log(a)*b*z)^(i+1)
3696          /(-(log(h)*(2*c*z+f)+2*log(a)*b*z)^2/(c*log(h)+log(a)*b))^((i+1)/2),
3697         i,0,n))
3698  /2));
3699 0;
3700
3701 /* Problem 623: NEW 10 */
3702 expand(niceindices(integrate(z^n*a^(b*sqrt(z))*h^(f*z+c*sqrt(z)),z))-
3703 (%e^-((c*log(h)+log(a)*b)^2/(4*f*log(h)))
3704  *2^(-2*n-1)
3705  *('sum(4^j*binomial(n,j)
3706            *'sum((c*log(h)+log(a)*b)^(2*n-j-i)*(-1)^(i-j)*binomial(j,i)
3707                                               *(2*f*log(h)*sqrt(z)
3708                                                +c*log(h)+log(a)*b)
3709                                                ^(j+i)
3710                                               *((c*log(h)+log(a)*b)
3711                                                *gamma_incomplete(
3712                                                 (j+i+1)/2,
3713                                                 -(2*f*log(h)*sqrt(z)
3714                                                  +c*log(h)+log(a)*b)
3715                                                  ^2
3716                                                  /(4*f*log(h)))
3717                                                *(2*f*log(h)*sqrt(z)
3718                                                 +c*log(h)+log(a)*b)
3719                                                +2*f*log(h)
3720                                                  *gamma_incomplete(
3721                                                   (j+i+2)/2,
3722                                                   -(2*f*log(h)*sqrt(z)
3723                                                    +c*log(h)+log(a)*b)
3724                                                    ^2
3725                                                    /(4*f*log(h)))
3726                                                  *sqrt(
3727                                                   -(2*f*log(h)*sqrt(z)
3728                                                    +c*log(h)+log(a)*b)
3729                                                    ^2
3730                                                    /(f*log(h))))
3731                   /(-(2*f*log(h)*sqrt(z)+c*log(h)+log(a)*b)^2/(f*log(h)))
3732                    ^((j+i+1)/2),i,0,j),j,0,n))
3733  /(f^(2*(n+1))*log(h)^(2*(n+1)))));
3734 0;
3735
3736 /* ----- Involving z^n*a^(b*z^r+e)*h^(c*z^r+f*z) ---------------------------- */
3737
3738 /* Problem 624: NEW 9 */
3739 expand(niceindices(integrate(z^n*a^(e+b*z^2)*h^(f*z+c*z^2),z))-
3740 (-a^e*%e^-(f^2*log(h)^2/(4*(c*log(h)+log(a)*b)))*(c*log(h)+log(a)*b)^(-n-1)
3741     *('sum(f^(n-i)*log(h)^(n-i)
3742                   *gamma_incomplete((i+1)/2,
3743                                     -(log(h)*(2*c*z+f)+2*log(a)*b*z)^2
3744                                      /(4*(c*log(h)+log(a)*b)))*(-1)^(i-n)
3745                   *2^(i-n)*binomial(n,i)*(log(h)*(2*c*z+f)+2*log(a)*b*z)^(i+1)
3746             /(-(log(h)*(2*c*z+f)+2*log(a)*b*z)^2/(c*log(h)+log(a)*b))
3747              ^((i+1)/2),i,0,n))
3748  /2));
3749 0;
3750
3751 /* Problem 625: NEW 10 */
3752 expand(niceindices(integrate(z^n*a^(e+b*sqrt(z))*h^(f*z+c*sqrt(z)),z))-
3753 (a^e*%e^-((c*log(h)+log(a)*b)^2/(4*f*log(h)))*2^(-2*n-1)
3754    *('sum(4^j*binomial(n,j)
3755              *'sum((c*log(h)+log(a)*b)^(2*n-j-i)*(-1)^(i-j)*binomial(j,i)
3756                                                 *(2*f*log(h)*sqrt(z)
3757                                                  +c*log(h)+log(a)*b)
3758                                                  ^(j+i)
3759                                                 *((c*log(h)+log(a)*b)
3760                                                  *gamma_incomplete(
3761                                                   (j+i+1)/2,
3762                                                   -(2*f*log(h)*sqrt(z)
3763                                                    +c*log(h)+log(a)*b)
3764                                                    ^2
3765                                                    /(4*f*log(h)))
3766                                                  *(2*f*log(h)*sqrt(z)
3767                                                   +c*log(h)+log(a)*b)
3768                                                  +2*f*log(h)
3769                                                    *gamma_incomplete(
3770                                                     (j+i+2)/2,
3771                                                     -(2*f*log(h)*sqrt(z)
3772                                                      +c*log(h)+log(a)*b)
3773                                                      ^2
3774                                                      /(4*f*log(h)))
3775                                                    *sqrt(
3776                                                     -(2*f*log(h)*sqrt(z)
3777                                                      +c*log(h)+log(a)*b)
3778                                                      ^2
3779                                                      /(f*log(h))))
3780                     /(-(2*f*log(h)*sqrt(z)+c*log(h)+log(a)*b)^2/(f*log(h)))
3781                      ^((j+i+1)/2),i,0,j),j,0,n))
3782  /(f^(2*(n+1))*log(h)^(2*(n+1)))));
3783 0;
3784
3785 /* ----- Involving z^n*a^(b*z^r+d*z)*h^(c*z^r+f*z) -------------------------- */
3786
3787 /* Problem 626: NEW 9 */
3788 expand(niceindices(integrate(z^n*a^(d*z+b*z^2)*h^(f*z+c*z^2),z))-
3789 (-%e^-((f*log(h)+log(a)*d)^2/(4*(c*log(h)+log(a)*b)))
3790  *(c*log(h)+log(a)*b)^(-n-1)
3791  *('sum((-f*log(h)-log(a)*d)^(n-i)*gamma_incomplete((i+1)/2,
3792                                                     -(log(h)*(2*c*z+f)
3793                                                      +log(a)*(2*b*z+d))
3794                                                      ^2
3795                                                      /(4*(c*log(h)+log(a)*b)))
3796                                   *2^(i-n)*binomial(n,i)
3797                                   *(log(h)*(2*c*z+f)+log(a)*(2*b*z+d))^(i+1)
3798          /(-(log(h)*(2*c*z+f)+log(a)*(2*b*z+d))^2/(c*log(h)+log(a)*b))
3799           ^((i+1)/2),i,0,n))
3800  /2));
3801 0;
3802
3803 /* Problem 627: NEW 10 */
3804 expand(niceindices(integrate(z^n*a^(d*z+b*sqrt(z))*h^(f*z+c*sqrt(z)),z))-
3805 (%e^-((c*log(h)+log(a)*b)^2/(4*(f*log(h)+log(a)*d)))
3806  *2^(-2*n-1)
3807  *('sum(4^j*binomial(n,j)
3808            *'sum((c*log(h)+log(a)*b)^(2*n-j-i)*(-1)^(i-j)*binomial(j,i)
3809                                               *(2*(f*log(h)+log(a)*d)*sqrt(z)
3810                                                +c*log(h)+log(a)*b)
3811                                                ^(j+i)
3812                                               *((c*log(h)+log(a)*b)
3813                                                *gamma_incomplete(
3814                                                 (j+i+1)/2,
3815                                                 -(2*(f*log(h)+log(a)*d)
3816                                                    *sqrt(z)
3817                                                  +c*log(h)+log(a)*b)
3818                                                  ^2
3819                                                  /(4*(f*log(h)+log(a)*d)))
3820                                                *(2*(f*log(h)+log(a)*d)*sqrt(z)
3821                                                 +c*log(h)+log(a)*b)
3822                                                +2*(f*log(h)+log(a)*d)
3823                                                  *gamma_incomplete(
3824                                                   (j+i+2)/2,
3825                                                   -(2*(f*log(h)+log(a)*d)
3826                                                      *sqrt(z)
3827                                                    +c*log(h)+log(a)*b)
3828                                                    ^2
3829                                                    /(4*(f*log(h)+log(a)*d)))
3830                                                  *sqrt(
3831                                                   -(2*(f*log(h)+log(a)*d)
3832                                                      *sqrt(z)
3833                                                    +c*log(h)+log(a)*b)
3834                                                    ^2
3835                                                    /(f*log(h)+log(a)*d)))
3836                   /(-(2*(f*log(h)+log(a)*d)*sqrt(z)+c*log(h)+log(a)*b)^2
3837                    /(f*log(h)+log(a)*d))
3838                    ^((j+i+1)/2),i,0,j),j,0,n))
3839  /(f*log(h)+log(a)*d)^(2*(n+1))));
3840 0;
3841
3842 /* ----- Involving z^n*a^(d*z)*h^(c*z^r+f*z+g) ------------------------------ */
3843
3844 /* Problem 628: NEW 9 */
3845 expand(niceindices(integrate(z^n*a^(d*z)*h^(g+f*z+c*z^2),z))-
3846 (-c^(-n-1)*h^g*%e^-((f*log(h)+log(a)*d)^2/(4*c*log(h)))*log(h)^(-n-1)
3847          *('sum((-f*log(h)-log(a)*d)^(n-i)
3848                  *gamma_incomplete((i+1)/2,
3849                                    -(log(h)*(2*c*z+f)+log(a)*d)^2
3850                                     /(4*c*log(h)))*2^(i-n)*binomial(n,i)
3851                  *(log(h)*(2*c*z+f)+log(a)*d)^(i+1)
3852                  /(-(log(h)*(2*c*z+f)+log(a)*d)^2/(c*log(h)))^((i+1)/2),i,0,
3853                 n))
3854  /2));
3855 0;
3856
3857 /* Problem 629: NEW 10 */
3858 expand(niceindices(integrate(z^n*a^(d*z)*h^(g+f*z+c*sqrt(z)),z))-
3859 (h^g*%e^-(c^2*log(h)^2/(4*(f*log(h)+log(a)*d)))*2^(-2*n-1)
3860    *('sum(4^j*binomial(n,j)
3861              *'sum(c^(2*n-j-i)*log(h)^(2*n-j-i)*(-1)^(i-j)*binomial(j,i)
3862                               *(2*(f*log(h)+log(a)*d)*sqrt(z)+c*log(h))^(j+i)
3863                               *(c*log(h)
3864                                  *gamma_incomplete((j+i+1)/2,
3865                                                    -(2*(f*log(h)+log(a)*d)
3866                                                       *sqrt(z)
3867                                                     +c*log(h))
3868                                                     ^2
3869                                                     /(4*(f*log(h)+log(a)*d)))
3870                                  *(2*(f*log(h)+log(a)*d)*sqrt(z)+c*log(h))
3871                                +2*(f*log(h)+log(a)*d)
3872                                  *gamma_incomplete((j+i+2)/2,
3873                                                    -(2*(f*log(h)+log(a)*d)
3874                                                       *sqrt(z)
3875                                                     +c*log(h))
3876                                                     ^2
3877                                                     /(4*(f*log(h)+log(a)*d)))
3878                                  *sqrt(-(2*(f*log(h)+log(a)*d)*sqrt(z)
3879                                         +c*log(h))
3880                                         ^2
3881                                         /(f*log(h)+log(a)*d)))
3882                     /(-(2*(f*log(h)+log(a)*d)*sqrt(z)+c*log(h))^2
3883                      /(f*log(h)+log(a)*d))
3884                      ^((j+i+1)/2),i,0,j),j,0,n))
3885  /(f*log(h)+log(a)*d)^(2*(n+1))));
3886 0;
3887 /* ----- Involving z^n*a^(d*z+e)*h^(c*z^r+f*z+g) ---------------------------- */
3888
3889 /* Problem 630: NEW 9 */
3890 expand(niceindices(integrate(z^n*a^(e+d*z)*h^(g+f*z+c*z^2),z))-
3891 (-a^e*c^(-n-1)*h^g*%e^-((f*log(h)+log(a)*d)^2/(4*c*log(h)))*log(h)^(-n-1)
3892     *('sum((-f*log(h)-log(a)*d)^(n-i)*gamma_incomplete((i+1)/2,
3893                                                        -(log(h)*(2*c*z+f)
3894                                                         +log(a)*d)
3895                                                         ^2
3896                                                         /(4*c*log(h)))*2^(i-n)
3897                                      *binomial(n,i)
3898                                      *(log(h)*(2*c*z+f)+log(a)*d)^(i+1)
3899             /(-(log(h)*(2*c*z+f)+log(a)*d)^2/(c*log(h)))^((i+1)/2),i,0,n))
3900  /2));
3901 0;
3902
3903 /* Problem 631: NEW 10 */
3904 expand(niceindices(integrate(z^n*a^(e+d*z)*h^(g+f*z+c*sqrt(z)),z))-
3905 (a^e*h^g*%e^-(c^2*log(h)^2/(4*(f*log(h)+log(a)*d)))*2^(-2*n-1)
3906    *('sum(4^j*binomial(n,j)
3907              *'sum(c^(2*n-j-i)*log(h)^(2*n-j-i)*(-1)^(i-j)*binomial(j,i)
3908                               *(2*(f*log(h)+log(a)*d)*sqrt(z)+c*log(h))^(j+i)
3909                               *(c*log(h)
3910                                  *gamma_incomplete((j+i+1)/2,
3911                                                    -(2*(f*log(h)+log(a)*d)
3912                                                       *sqrt(z)
3913                                                     +c*log(h))
3914                                                     ^2
3915                                                     /(4*(f*log(h)+log(a)*d)))
3916                                  *(2*(f*log(h)+log(a)*d)*sqrt(z)+c*log(h))
3917                                +2*(f*log(h)+log(a)*d)
3918                                  *gamma_incomplete((j+i+2)/2,
3919                                                    -(2*(f*log(h)+log(a)*d)
3920                                                       *sqrt(z)
3921                                                     +c*log(h))
3922                                                     ^2
3923                                                     /(4*(f*log(h)+log(a)*d)))
3924                                  *sqrt(-(2*(f*log(h)+log(a)*d)*sqrt(z)
3925                                         +c*log(h))
3926                                         ^2
3927                                         /(f*log(h)+log(a)*d)))
3928                     /(-(2*(f*log(h)+log(a)*d)*sqrt(z)+c*log(h))^2
3929                      /(f*log(h)+log(a)*d))
3930                      ^((j+i+1)/2),i,0,j),j,0,n))
3931  /(f*log(h)+log(a)*d)^(2*(n+1))));
3932 0;
3933
3934 /* ----- Involving z^n*a^(b*z^r)*h^(c*z^r+f*z+g) ---------------------------- */
3935
3936 /* Problem 632: NEW 9 */
3937 expand(niceindices(integrate(z^n*a^(b*z^2)*h^(g+f*z+c*z^2),z))-
3938 (-h^g*%e^-(f^2*log(h)^2/(4*(c*log(h)+log(a)*b)))*(c*log(h)+log(a)*b)^(-n-1)
3939     *('sum(f^(n-i)*log(h)^(n-i)
3940                   *gamma_incomplete((i+1)/2,
3941                                     -(log(h)*(2*c*z+f)+2*log(a)*b*z)^2
3942                                      /(4*(c*log(h)+log(a)*b)))*(-1)^(i-n)
3943                   *2^(i-n)*binomial(n,i)*(log(h)*(2*c*z+f)+2*log(a)*b*z)^(i+1)
3944             /(-(log(h)*(2*c*z+f)+2*log(a)*b*z)^2/(c*log(h)+log(a)*b))
3945              ^((i+1)/2),i,0,n))
3946  /2));
3947 0;
3948
3949 /* Problem 633: NEW 10 */
3950 expand(niceindices(integrate(z^n*a^(b*sqrt(z))*h^(g+f*z+c*sqrt(z)),z))-
3951 (h^g*%e^-((c*log(h)+log(a)*b)^2/(4*f*log(h)))*2^(-2*n-1)
3952    *('sum(4^j*binomial(n,j)
3953              *'sum((c*log(h)+log(a)*b)^(2*n-j-i)*(-1)^(i-j)*binomial(j,i)
3954                                                 *(2*f*log(h)*sqrt(z)
3955                                                  +c*log(h)+log(a)*b)
3956                                                  ^(j+i)
3957                                                 *((c*log(h)+log(a)*b)
3958                                                  *gamma_incomplete(
3959                                                   (j+i+1)/2,
3960                                                   -(2*f*log(h)*sqrt(z)
3961                                                    +c*log(h)+log(a)*b)
3962                                                    ^2
3963                                                    /(4*f*log(h)))
3964                                                  *(2*f*log(h)*sqrt(z)
3965                                                   +c*log(h)+log(a)*b)
3966                                                  +2*f*log(h)
3967                                                    *gamma_incomplete(
3968                                                     (j+i+2)/2,
3969                                                     -(2*f*log(h)*sqrt(z)
3970                                                      +c*log(h)+log(a)*b)
3971                                                      ^2
3972                                                      /(4*f*log(h)))
3973                                                    *sqrt(
3974                                                     -(2*f*log(h)*sqrt(z)
3975                                                      +c*log(h)+log(a)*b)
3976                                                      ^2
3977                                                      /(f*log(h))))
3978                     /(-(2*f*log(h)*sqrt(z)+c*log(h)+log(a)*b)^2/(f*log(h)))
3979                      ^((j+i+1)/2),i,0,j),j,0,n))
3980  /(f^(2*(n+1))*log(h)^(2*(n+1)))));
3981 0;
3982
3983 /* ----- Involving z^n*a^(b*z^r+e)*h^(c*z^r+f*z+g) -------------------------- */
3984
3985 /* Problem 634: NEW 9 */
3986 expand(niceindices(integrate(z^n*a^(e+b*z^2)*h^(g+f*z+c*z^2),z))-
3987 (-a^e*h^g*%e^-(f^2*log(h)^2/(4*(c*log(h)+log(a)*b)))*(c*log(h)+log(a)*b)^(-n-1)
3988     *('sum(f^(n-i)*log(h)^(n-i)
3989                   *gamma_incomplete((i+1)/2,
3990                                     -(log(h)*(2*c*z+f)+2*log(a)*b*z)^2
3991                                      /(4*(c*log(h)+log(a)*b)))*(-1)^(i-n)
3992                   *2^(i-n)*binomial(n,i)*(log(h)*(2*c*z+f)+2*log(a)*b*z)^(i+1)
3993             /(-(log(h)*(2*c*z+f)+2*log(a)*b*z)^2/(c*log(h)+log(a)*b))
3994              ^((i+1)/2),i,0,n))
3995  /2));
3996 0;
3997
3998 /* Problem 635: NEW 10 */
3999 expand(niceindices(integrate(z^n*a^(e+b*sqrt(z))*h^(g+f*z+c*sqrt(z)),z))-
4000 (a^e*h^g*%e^-((c*log(h)+log(a)*b)^2/(4*f*log(h)))*2^(-2*n-1)
4001    *('sum(4^j*binomial(n,j)
4002              *'sum((c*log(h)+log(a)*b)^(2*n-j-i)*(-1)^(i-j)*binomial(j,i)
4003                                                 *(2*f*log(h)*sqrt(z)
4004                                                  +c*log(h)+log(a)*b)
4005                                                  ^(j+i)
4006                                                 *((c*log(h)+log(a)*b)
4007                                                  *gamma_incomplete(
4008                                                   (j+i+1)/2,
4009                                                   -(2*f*log(h)*sqrt(z)
4010                                                    +c*log(h)+log(a)*b)
4011                                                    ^2
4012                                                    /(4*f*log(h)))
4013                                                  *(2*f*log(h)*sqrt(z)
4014                                                   +c*log(h)+log(a)*b)
4015                                                  +2*f*log(h)
4016                                                    *gamma_incomplete(
4017                                                     (j+i+2)/2,
4018                                                     -(2*f*log(h)*sqrt(z)
4019                                                      +c*log(h)+log(a)*b)
4020                                                      ^2
4021                                                      /(4*f*log(h)))
4022                                                    *sqrt(
4023                                                     -(2*f*log(h)*sqrt(z)
4024                                                      +c*log(h)+log(a)*b)
4025                                                      ^2
4026                                                      /(f*log(h))))
4027                     /(-(2*f*log(h)*sqrt(z)+c*log(h)+log(a)*b)^2/(f*log(h)))
4028                      ^((j+i+1)/2),i,0,j),j,0,n))
4029  /(f^(2*(n+1))*log(h)^(2*(n+1)))));
4030 0;
4031
4032 /* ----- Involving z^n*a^(b*z^r+d*z)*h^(c*z^r+f*z+g) ------------------------ */
4033
4034 /* Problem 636: NEW 9 */
4035 expand(niceindices(integrate(z^n*a^(d*z+b*z^2)*h^(g+f*z+c*z^2),z))-
4036 (-h^g*%e^-((f*log(h)+log(a)*d)^2/(4*(c*log(h)+log(a)*b)))
4037     *(c*log(h)+log(a)*b)^(-n-1)
4038     *('sum((-f*log(h)-log(a)*d)^(n-i)*gamma_incomplete((i+1)/2,
4039                                                        -(log(h)*(2*c*z+f)
4040                                                         +log(a)*(2*b*z+d))
4041                                                         ^2
4042                                                         /(4
4043                                                          *(c*log(h)
4044                                                           +log(a)*b)))*2^(i-n)
4045                                      *binomial(n,i)
4046                                      *(log(h)*(2*c*z+f)+log(a)*(2*b*z+d))
4047                                       ^(i+1)
4048             /(-(log(h)*(2*c*z+f)+log(a)*(2*b*z+d))^2/(c*log(h)+log(a)*b))
4049              ^((i+1)/2),i,0,n))/2));
4050 0;
4051
4052 /* Problem 637: NEW 10 */
4053 expand(niceindices(integrate(z^n*a^(d*z+b*sqrt(z))*h^(g+f*z+c*sqrt(z)),z))-
4054 (h^g*%e^-((c*log(h)+log(a)*b)^2/(4*(f*log(h)+log(a)*d)))*2^(-2*n-1)
4055    *('sum(4^j*binomial(n,j)
4056              *'sum((c*log(h)+log(a)*b)^(2*n-j-i)*(-1)^(i-j)*binomial(j,i)
4057                                                 *(2*(f*log(h)+log(a)*d)
4058                                                    *sqrt(z)
4059                                                  +c*log(h)+log(a)*b)
4060                                                  ^(j+i)
4061                                                 *((c*log(h)+log(a)*b)
4062                                                  *gamma_incomplete(
4063                                                   (j+i+1)/2,
4064                                                   -(2*(f*log(h)+log(a)*d)
4065                                                      *sqrt(z)
4066                                                    +c*log(h)+log(a)*b)
4067                                                    ^2
4068                                                    /(4*(f*log(h)+log(a)*d)))
4069                                                  *(2*(f*log(h)+log(a)*d)
4070                                                     *sqrt(z)
4071                                                   +c*log(h)+log(a)*b)
4072                                                  +2*(f*log(h)+log(a)*d)
4073                                                    *gamma_incomplete(
4074                                                     (j+i+2)/2,
4075                                                     -(2*(f*log(h)+log(a)*d)
4076                                                        *sqrt(z)
4077                                                      +c*log(h)+log(a)*b)
4078                                                      ^2
4079                                                      /(4*(f*log(h)+log(a)*d)))
4080                                                    *sqrt(
4081                                                     -(2*(f*log(h)+log(a)*d)
4082                                                        *sqrt(z)
4083                                                      +c*log(h)+log(a)*b)
4084                                                      ^2
4085                                                      /(f*log(h)+log(a)*d)))
4086                     /(-(2*(f*log(h)+log(a)*d)*sqrt(z)+c*log(h)+log(a)*b)^2
4087                      /(f*log(h)+log(a)*d))
4088                      ^((j+i+1)/2),i,0,j),j,0,n))
4089  /(f*log(h)+log(a)*d)^(2*(n+1))));
4090 0;
4091
4092 /* ----- Involving z^n*a^(b*z^r+d*z+e)*h^(c*z^r+f*z+g) ---------------------- */
4093
4094 /* Problem 638: NEW 9 */
4095 expand(niceindices(integrate(z^n*a^(e+d*z+b*z^2)*h^(g+f*z+c*z^2),z))-
4096 (-a^e*h^g*%e^-((f*log(h)+log(a)*d)^2/(4*(c*log(h)+log(a)*b)))
4097     *(c*log(h)+log(a)*b)^(-n-1)
4098     *('sum((-f*log(h)-log(a)*d)^(n-i)*gamma_incomplete((i+1)/2,
4099                                                        -(log(h)*(2*c*z+f)
4100                                                         +log(a)*(2*b*z+d))
4101                                                         ^2
4102                                                         /(4
4103                                                          *(c*log(h)
4104                                                           +log(a)*b)))*2^(i-n)
4105                                      *binomial(n,i)
4106                                      *(log(h)*(2*c*z+f)+log(a)*(2*b*z+d))
4107                                       ^(i+1)
4108             /(-(log(h)*(2*c*z+f)+log(a)*(2*b*z+d))^2/(c*log(h)+log(a)*b))
4109              ^((i+1)/2),i,0,n))
4110  /2));
4111 0;
4112
4113 /* Problem 639: NEW 10 */
4114 expand(niceindices(integrate(z^n*a^(e+d*z+b*sqrt(z))*h^(g+f*z+c*sqrt(z)),z))-
4115 (a^e*h^g*%e^-((c*log(h)+log(a)*b)^2/(4*(f*log(h)+log(a)*d)))*2^(-2*n-1)
4116    *('sum(4^j*binomial(n,j)
4117              *'sum((c*log(h)+log(a)*b)^(2*n-j-i)*(-1)^(i-j)*binomial(j,i)
4118                                                 *(2*(f*log(h)+log(a)*d)
4119                                                    *sqrt(z)
4120                                                  +c*log(h)+log(a)*b)
4121                                                  ^(j+i)
4122                                                 *((c*log(h)+log(a)*b)
4123                                                  *gamma_incomplete(
4124                                                   (j+i+1)/2,
4125                                                   -(2*(f*log(h)+log(a)*d)
4126                                                      *sqrt(z)
4127                                                    +c*log(h)+log(a)*b)
4128                                                    ^2
4129                                                    /(4*(f*log(h)+log(a)*d)))
4130                                                  *(2*(f*log(h)+log(a)*d)
4131                                                     *sqrt(z)
4132                                                   +c*log(h)+log(a)*b)
4133                                                  +2*(f*log(h)+log(a)*d)
4134                                                    *gamma_incomplete(
4135                                                     (j+i+2)/2,
4136                                                     -(2*(f*log(h)+log(a)*d)
4137                                                        *sqrt(z)
4138                                                      +c*log(h)+log(a)*b)
4139                                                      ^2
4140                                                      /(4*(f*log(h)+log(a)*d)))
4141                                                    *sqrt(
4142                                                     -(2*(f*log(h)+log(a)*d)
4143                                                        *sqrt(z)
4144                                                      +c*log(h)+log(a)*b)
4145                                                      ^2
4146                                                      /(f*log(h)+log(a)*d)))
4147                     /(-(2*(f*log(h)+log(a)*d)*sqrt(z)+c*log(h)+log(a)*b)^2
4148                      /(f*log(h)+log(a)*d))
4149                      ^((j+i+1)/2),i,0,j),j,0,n))
4150  /(f*log(h)+log(a)*d)^(2*(n+1))));
4151 0;
4152
4153 /* ----- Products of powers of the direct function and a power function ----- */
4154
4155 /* ----- Involving z^(v-1)*%e^(c*z)*(%e^(a*z))^u ---------------------------- */
4156
4157 /* Problem 640: NEW 7-1*/
4158 expand(integrate(z^(v-1)*%e^(c*z)*(%e^(a*z))^u,z)-
4159 -gamma_incomplete(v,-(a*u+c)*z)*z^v*(%e^(a*z))^u*%e^(c*z-(a*u+c)*z)
4160  /(-(a*u+c)*z)^v)$
4161 0;
4162
4163 /* Problem 641: NEW 7-1 */
4164 expand(integrate(z^n*%e^(c*z)*(%e^(a*z))^u,z)-
4165 -(-1)^(n+1)*gamma_incomplete(n+1,-(a*u+c)*z)*(a*u+c)^(-n-1)*(%e^(a*z))^u
4166            *%e^(c*z-(a*u+c)*z))$
4167 0;
4168
4169 /* Problem 642: NEW 7-1 */
4170 expand(integrate(z^(1/2+n)*%e^(c*z)*(%e^(a*z))^u,z)-
4171 -gamma_incomplete(n+3/2,-(a*u+c)*z)*z^(n+3/2)*(-(a*u+c)*z)^(-n-3/2)
4172                                    *(%e^(a*z))^u*%e^(c*z-(a*u+c)*z))$
4173 0;
4174
4175 /* ----- Involving z^(v-1)*%e^(c*z+d)*(%e^(a*z))^u -------------------------- */
4176
4177 /* Problem 643: NEW 7-1 */
4178 expand(integrate(z^(v-1)*%e^(c*z+d)*(%e^(a*z))^u,z)-
4179 -gamma_incomplete(v,-(a*u+c)*z)*z^v*(%e^(a*z))^u*%e^(-(a*u+c)*z+c*z+d)
4180  /(-(a*u+c)*z)^v)$
4181 0;
4182
4183 /* Problem 644: NEW 7-1 */
4184 expand(integrate(z^n*%e^(c*z+d)*(%e^(a*z))^u,z)-
4185 -(-1)^(n+1)*gamma_incomplete(n+1,-(a*u+c)*z)*(a*u+c)^(-n-1)*(%e^(a*z))^u
4186            *%e^(-(a*u+c)*z+c*z+d));
4187 0;
4188
4189 /* Problem 645: NEW 7-1 */
4190 expand(integrate(z^(1/2+n)*%e^(c*z+d)*(%e^(a*z))^u,z)-
4191 -gamma_incomplete(n+3/2,-(a*u+c)*z)*z^(n+3/2)*(-(a*u+c)*z)^(-n-3/2)
4192                                    *(%e^(a*z))^u*%e^(-(a*u+c)*z+c*z+d))$
4193 0;
4194
4195 /* ----- Involving z^(v-1)*%e^(c*z)*(%e^(a*z+b))^u -------------------------- */
4196
4197 /* Problem 646: NEW 7-1 */
4198 expand(integrate(z^(v-1)*%e^(c*z)*(%e^(a*z+b))^u,z)-
4199 -gamma_incomplete(v,-(a*u+c)*z)*z^v*(%e^(a*z+b))^u*%e^(c*z-(a*u+c)*z)
4200  /(-(a*u+c)*z)^v);
4201 0;
4202
4203 /* Problem 647: NEW 7-1 */
4204 expand(integrate(z^n*%e^(c*z)*(%e^(a*z+b))^u,z)-
4205 -(-1)^(n+1)*gamma_incomplete(n+1,-(a*u+c)*z)*(a*u+c)^(-n-1)*(%e^(a*z+b))^u
4206            *%e^(c*z-(a*u+c)*z))$
4207 0;
4208
4209 /* Problem 648: NEW 7-1 */
4210 expand(integrate(z^(1/2+n)*%e^(c*z)*(%e^(a*z+b))^u,z)-
4211 -gamma_incomplete(n+3/2,-(a*u+c)*z)*z^(n+3/2)*(-(a*u+c)*z)^(-n-3/2)
4212                                    *(%e^(a*z+b))^u*%e^(c*z-(a*u+c)*z))$
4213 0;
4214
4215 /* ----- Involving z^(v-1)*%e^(c*z+d)*(%e^(a*z+b))^u ------------------------ */
4216
4217 /* Problem 649: NEW 7-1 */
4218 expand(integrate(z^(v-1)*%e^(c*z+d)*(%e^(a*z+b))^u,z)-
4219 -gamma_incomplete(v,-(a*u+c)*z)*z^v*(%e^(a*z+b))^u*%e^(-(a*u+c)*z+c*z+d)
4220  /(-(a*u+c)*z)^v)$
4221 0;
4222
4223 /* Problem 650: NEW 7-1 */
4224 expand(integrate(z^n*%e^(c*z+d)*(%e^(a*z+b))^u,z)-
4225 -(-1)^(n+1)*gamma_incomplete(n+1,-(a*u+c)*z)*(a*u+c)^(-n-1)*(%e^(a*z+b))^u
4226            *%e^(-(a*u+c)*z+c*z+d))$
4227 0;
4228
4229 /* Problem 651: NEW 7-1 */
4230 expand(integrate(z^(1/2+n)*%e^(c*z+d)*(%e^(a*z+b))^u,z)-
4231 -gamma_incomplete(n+3/2,-(a*u+c)*z)*z^(n+3/2)*(-(a*u+c)*z)^(-n-3/2)
4232                                    *(%e^(a*z+b))^u*%e^(-(a*u+c)*z+c*z+d))$
4233 0;
4234
4235 /* ----- Involving z^n*%e^(b*z^r)*(%e^(c*z))^u ------------------------------ */
4236
4237 /* Problem 652: NEW 9-1 */
4238 expand(niceindices(integrate(z^n*%e^(b*z^2)*(%e^(c*z))^u,z))-
4239 (-b^(-n-1)*(%e^(c*z))^u*%e^(b*z^2-z*(b*z+c*u)-c^2*u^2/(4*b))
4240          *('sum(c^(n-i)*gamma_incomplete((i+1)/2,-(2*b*z+c*u)^2/(4*b))
4241                        *(-1)^(i-n)*2^(i-n)*binomial(n,i)*u^(n-i)
4242                        *(2*b*z+c*u)^(i+1)
4243                  /(-(2*b*z+c*u)^2/b)^((i+1)/2),i,0,n))
4244  /2));
4245 0;
4246
4247 /* Problem 653: NEW 10-1 */
4248 expand(niceindices(integrate(z^n*%e^(b*sqrt(z))*(%e^(c*z))^u,z))-
4249 (2^(-2*n-1)*('sum(4^j*binomial(n,j)
4250                     *'sum(b^(2*n-j-i)*(-1)^(i-j)*binomial(j,i)
4251                                      *(2*c*u*sqrt(z)+b)^(j+i)
4252                                      *(b
4253                                       *gamma_incomplete((j+i+1)/2,
4254                                                         -(2*c*u*sqrt(z)+b)^2
4255                                                          /(4*c*u))
4256                                       *(2*c*u*sqrt(z)+b)
4257                                       +2*c
4258                                         *gamma_incomplete((j+i+2)/2,
4259                                                           -(2*c*u*sqrt(z)+b)^2
4260                                                            /(4*c*u))*u
4261                                         *sqrt((2*c*u*sqrt(z)+b)^2/(c*u)))
4262                            /(-(2*c*u*sqrt(z)+b)^2/(c*u))^((j+i+1)/2),i,0,j),j,
4263                  0,n))*(%e^(c*z))^u*%e^(-c*u*z-b^2/(4*c*u))
4264  /(c^(2*(n+1))*u^(2*(n+1)))));
4265 0;
4266
4267 /* ----- Involving z^n*%e^(b*z^r+e)*(%e^(c*z))^u ---------------------------- */
4268
4269 /* Problem 654: NEW 9-1 */
4270 expand(niceindices(integrate(z^n*%e^(e+b*z^2)*(%e^(c*z))^u,z))-
4271 (-b^(-n-1)*(%e^(c*z))^u*%e^(b*z^2-z*(b*z+c*u)-c^2*u^2/(4*b)+e)
4272          *('sum(c^(n-i)*gamma_incomplete((i+1)/2,-(2*b*z+c*u)^2/(4*b))
4273                        *(-1)^(i-n)*2^(i-n)*binomial(n,i)*u^(n-i)
4274                        *(2*b*z+c*u)^(i+1)
4275                  /(-(2*b*z+c*u)^2/b)^((i+1)/2),i,0,n))
4276  /2));
4277 0;
4278
4279 /* Problem 655: NEW 10-1 */
4280 expand(niceindices(integrate(z^n*%e^(e+b*sqrt(z))*(%e^(c*z))^u,z))-
4281 (2^(-2*n-1)*('sum(4^j*binomial(n,j)
4282                     *'sum(b^(2*n-j-i)*(-1)^(i-j)*binomial(j,i)
4283                                      *(2*c*u*sqrt(z)+b)^(j+i)
4284                                      *(b
4285                                       *gamma_incomplete((j+i+1)/2,
4286                                                         -(2*c*u*sqrt(z)+b)^2
4287                                                          /(4*c*u))
4288                                       *(2*c*u*sqrt(z)+b)
4289                                       +2*c
4290                                         *gamma_incomplete((j+i+2)/2,
4291                                                           -(2*c*u*sqrt(z)+b)^2
4292                                                            /(4*c*u))*u
4293                                         *sqrt((2*c*u*sqrt(z)+b)^2/(c*u)))
4294                            /(-(2*c*u*sqrt(z)+b)^2/(c*u))^((j+i+1)/2),i,0,j),j,
4295                  0,n))*(%e^(c*z))^u*%e^(-c*u*z-b^2/(4*c*u)+e)
4296  /(c^(2*(n+1))*u^(2*(n+1)))));
4297 0;
4298
4299 /* ----- Involving z^n*%e^(b*z^r+d*z)*(%e^(c*z))^u -------------------------- */
4300
4301 /* Problem 656: NEW 9-1 */
4302 expand(niceindices(integrate(z^n*%e^(d*z+b*z^2)*(%e^(c*z))^u,z))-
4303 (-b^(-n-1)*(%e^(c*z))^u*%e^(-z*(b*z+c*u+d)+z*(b*z+d)-(c*u+d)^2/(4*b))
4304          *('sum(gamma_incomplete((i+1)/2,-(2*b*z+c*u+d)^2/(4*b))
4305                  *2^(i-n)*binomial(n,i)*(-c*u-d)^(n-i)*(2*b*z+c*u+d)^(i+1)
4306                  /(-(2*b*z+c*u+d)^2/b)^((i+1)/2),i,0,n))
4307  /2));
4308 0;
4309
4310 /* Problem 657: NEW 10-1 */
4311 expand(niceindices(integrate(z^n*%e^(d*z+b*sqrt(z))*(%e^(c*z))^u,z))-
4312 (2^(-2*n-1)*('sum(4^j*binomial(n,j)
4313                     *'sum(b^(2*n-j-i)*(-1)^(i-j)*binomial(j,i)
4314                                      *(2*(c*u+d)*sqrt(z)+b)^(j+i)
4315                                      *(b
4316                                       *gamma_incomplete((j+i+1)/2,
4317                                                         -(2*(c*u+d)*sqrt(z)+b)
4318                                                          ^2
4319                                                          /(4*(c*u+d)))
4320                                       *(2*(c*u+d)*sqrt(z)+b)
4321                                       +2
4322                                        *gamma_incomplete((j+i+2)/2,
4323                                                          -(2*(c*u+d)*sqrt(z)
4324                                                           +b)
4325                                                           ^2
4326                                                           /(4*(c*u+d)))
4327                                        *(c*u+d)
4328                                        *sqrt((2*(c*u+d)*sqrt(z)+b)^2/(c*u+d)))
4329                            /((2*(c*u+d)*sqrt(z)+b)^2/(-c*u-d))^((j+i+1)/2),i,
4330                           0,j),j,0,n))*(%e^(c*z))^u
4331           *%e^(-c*u*z-b^2/(4*(c*u+d)))
4332  /(c*u+d)^(2*(n+1))));
4333 0;
4334
4335 /* ----- Involving z^n*%e^(b*z^r+d*z+e)*(%e^(c*z^r))^u ---------------------- */
4336
4337 /* Problem 658: NEW 9-1 */
4338 expand(niceindices(integrate(z^n*%e^(e+d*z+b*z^2)*(%e^(c*z))^u,z))-
4339 (-b^(-n-1)*(%e^(c*z))^u*%e^(-z*(b*z+c*u+d)+z*(b*z+d)-(c*u+d)^2/(4*b)+e)
4340          *('sum(gamma_incomplete((i+1)/2,-(2*b*z+c*u+d)^2/(4*b))
4341                  *2^(i-n)*binomial(n,i)*(-c*u-d)^(n-i)*(2*b*z+c*u+d)^(i+1)
4342                  /(-(2*b*z+c*u+d)^2/b)^((i+1)/2),i,0,n))
4343  /2));
4344 0;
4345
4346 /* Problem 659: NEW 10-1 */
4347 expand(niceindices(integrate(z^n*%e^(e+d*z+b*sqrt(z))*(%e^(c*z))^u,z))-
4348 (2^(-2*n-1)*('sum(4^j*binomial(n,j)
4349                     *'sum(b^(2*n-j-i)*(-1)^(i-j)*binomial(j,i)
4350                                      *(2*(c*u+d)*sqrt(z)+b)^(j+i)
4351                                      *(b
4352                                       *gamma_incomplete((j+i+1)/2,
4353                                                         -(2*(c*u+d)*sqrt(z)+b)
4354                                                          ^2
4355                                                          /(4*(c*u+d)))
4356                                       *(2*(c*u+d)*sqrt(z)+b)
4357                                       +2
4358                                        *gamma_incomplete((j+i+2)/2,
4359                                                          -(2*(c*u+d)*sqrt(z)
4360                                                           +b)
4361                                                           ^2
4362                                                           /(4*(c*u+d)))
4363                                        *(c*u+d)
4364                                        *sqrt((2*(c*u+d)*sqrt(z)+b)^2/(c*u+d)))
4365                            /((2*(c*u+d)*sqrt(z)+b)^2/(-c*u-d))^((j+i+1)/2),i,
4366                           0,j),j,0,n))*(%e^(c*z))^u
4367           *%e^(-c*u*z-b^2/(4*(c*u+d))+e)
4368  /(c*u+d)^(2*(n+1))));
4369 0;
4370
4371 /* ----- Involving z^n*%e^(b*z^r)*(%e^(f*z+g))^u ---------------------------- */
4372
4373 /* Problem 660: NEW 9-1 */
4374 expand(niceindices(integrate(z^n*%e^(b*z^2)*(%e^(g+f*z))^u,z))-
4375 (-b^(-n-1)*(%e^(f*z+g))^u*%e^(b*z^2-z*(b*z+f*u)-f^2*u^2/(4*b))
4376          *('sum(f^(n-i)*gamma_incomplete((i+1)/2,-(2*b*z+f*u)^2/(4*b))
4377                        *(-1)^(i-n)*2^(i-n)*binomial(n,i)*u^(n-i)
4378                        *(2*b*z+f*u)^(i+1)
4379                  /(-(2*b*z+f*u)^2/b)^((i+1)/2),i,0,n))
4380  /2));
4381 0;
4382
4383 /* Problem 661: NEW 10-1 */
4384 expand(niceindices(integrate(z^n*%e^(b*sqrt(z))*(%e^(g+f*z))^u,z))-
4385 (2^(-2*n-1)*('sum(4^j*binomial(n,j)
4386                     *'sum(b^(2*n-j-i)*(-1)^(i-j)*binomial(j,i)
4387                                      *(2*f*u*sqrt(z)+b)^(j+i)
4388                                      *(b
4389                                       *gamma_incomplete((j+i+1)/2,
4390                                                         -(2*f*u*sqrt(z)+b)^2
4391                                                          /(4*f*u))
4392                                       *(2*f*u*sqrt(z)+b)
4393                                       +2*f
4394                                         *gamma_incomplete((j+i+2)/2,
4395                                                           -(2*f*u*sqrt(z)+b)^2
4396                                                            /(4*f*u))*u
4397                                         *sqrt((2*f*u*sqrt(z)+b)^2/(f*u)))
4398                            /(-(2*f*u*sqrt(z)+b)^2/(f*u))^((j+i+1)/2),i,0,j),j,
4399                  0,n))*(%e^(f*z+g))^u*%e^(-f*u*z-b^2/(4*f*u))
4400  /(f^(2*(n+1))*u^(2*(n+1)))));
4401 0;
4402
4403 /* ----- Involving z^n*%e^(b*z^r+e)*(%e^(f*z+g))^u -------------------------- */
4404
4405 /* Problem 662: NEW 9-1 */
4406 expand(niceindices(integrate(z^n*%e^(e+b*z^2)*(%e^(g+f*z))^u,z))-
4407 (-b^(-n-1)*(%e^(f*z+g))^u*%e^(b*z^2-z*(b*z+f*u)-f^2*u^2/(4*b)+e)
4408          *('sum(f^(n-i)*gamma_incomplete((i+1)/2,-(2*b*z+f*u)^2/(4*b))
4409                        *(-1)^(i-n)*2^(i-n)*binomial(n,i)*u^(n-i)
4410                        *(2*b*z+f*u)^(i+1)
4411                  /(-(2*b*z+f*u)^2/b)^((i+1)/2),i,0,n))
4412  /2));
4413 0;
4414
4415 /* Problem 663: NEW 10-1 */
4416 expand(niceindices(integrate(z^n*%e^(e+b*sqrt(z))*(%e^(g+f*z))^u,z))-
4417 (2^(-2*n-1)*('sum(4^j*binomial(n,j)
4418                     *'sum(b^(2*n-j-i)*(-1)^(i-j)*binomial(j,i)
4419                                      *(2*f*u*sqrt(z)+b)^(j+i)
4420                                      *(b
4421                                       *gamma_incomplete((j+i+1)/2,
4422                                                         -(2*f*u*sqrt(z)+b)^2
4423                                                          /(4*f*u))
4424                                       *(2*f*u*sqrt(z)+b)
4425                                       +2*f
4426                                         *gamma_incomplete((j+i+2)/2,
4427                                                           -(2*f*u*sqrt(z)+b)^2
4428                                                            /(4*f*u))*u
4429                                         *sqrt((2*f*u*sqrt(z)+b)^2/(f*u)))
4430                            /(-(2*f*u*sqrt(z)+b)^2/(f*u))^((j+i+1)/2),i,0,j),j,
4431                  0,n))*(%e^(f*z+g))^u*%e^(-f*u*z-b^2/(4*f*u)+e)
4432  /(f^(2*(n+1))*u^(2*(n+1)))));
4433 0;
4434
4435 /* ----- Involving z^n*%e^(b*z^r+d*z)*(%e^(f*z+g))^u ------------------------ */
4436
4437 /* Problem 664: NEW 9-1 */
4438 expand(niceindices(integrate(z^n*%e^(d*z+b*z^2)*(%e^(g+f*z))^u,z))-
4439 (-b^(-n-1)*(%e^(f*z+g))^u*%e^(-z*(b*z+f*u+d)+z*(b*z+d)-(f*u+d)^2/(4*b))
4440          *('sum(gamma_incomplete((i+1)/2,-(2*b*z+f*u+d)^2/(4*b))
4441                  *2^(i-n)*binomial(n,i)*(-f*u-d)^(n-i)*(2*b*z+f*u+d)^(i+1)
4442                  /(-(2*b*z+f*u+d)^2/b)^((i+1)/2),i,0,n))
4443  /2));
4444 0;
4445
4446 /* Problem 665: NEW 10-1 */
4447 expand(niceindices(integrate(z^n*%e^(d*z+b*sqrt(z))*(%e^(g+f*z))^u,z))-
4448 (2^(-2*n-1)*('sum(4^j*binomial(n,j)
4449                     *'sum(b^(2*n-j-i)*(-1)^(i-j)*binomial(j,i)
4450                                      *(2*(f*u+d)*sqrt(z)+b)^(j+i)
4451                                      *(b
4452                                       *gamma_incomplete((j+i+1)/2,
4453                                                         -(2*(f*u+d)*sqrt(z)+b)
4454                                                          ^2
4455                                                          /(4*(f*u+d)))
4456                                       *(2*(f*u+d)*sqrt(z)+b)
4457                                       +2
4458                                        *gamma_incomplete((j+i+2)/2,
4459                                                          -(2*(f*u+d)*sqrt(z)
4460                                                           +b)
4461                                                           ^2
4462                                                           /(4*(f*u+d)))
4463                                        *(f*u+d)
4464                                        *sqrt((2*(f*u+d)*sqrt(z)+b)^2/(f*u+d)))
4465                            /((2*(f*u+d)*sqrt(z)+b)^2/(-f*u-d))^((j+i+1)/2),i,
4466                           0,j),j,0,n))*(%e^(f*z+g))^u
4467           *%e^(-f*u*z-b^2/(4*(f*u+d)))
4468  /(f*u+d)^(2*(n+1))));
4469 0;
4470
4471 /* ----- Involving z^n*%e^(b*z^r+d*z+e)*(%e^(f*z+g))^u ---------------------- */
4472
4473 /* Problem 666: NEW 9-1 */
4474 expand(niceindices(integrate(z^n*%e^(e+d*z+b*z^2)*(%e^(g+f*z))^u,z))-
4475 (-b^(-n-1)*(%e^(f*z+g))^u*%e^(-z*(b*z+f*u+d)+z*(b*z+d)-(f*u+d)^2/(4*b)+e)
4476          *('sum(gamma_incomplete((i+1)/2,-(2*b*z+f*u+d)^2/(4*b))
4477                  *2^(i-n)*binomial(n,i)*(-f*u-d)^(n-i)*(2*b*z+f*u+d)^(i+1)
4478                  /(-(2*b*z+f*u+d)^2/b)^((i+1)/2),i,0,n))
4479  /2));
4480 0;
4481
4482 /* Problem 667: NEW 10-1 */
4483 expand(niceindices(integrate(z^n*%e^(e+d*z+b*sqrt(z))*(%e^(g+f*z))^u,z))-
4484 (2^(-2*n-1)*('sum(4^j*binomial(n,j)
4485                     *'sum(b^(2*n-j-i)*(-1)^(i-j)*binomial(j,i)
4486                                      *(2*(f*u+d)*sqrt(z)+b)^(j+i)
4487                                      *(b
4488                                       *gamma_incomplete((j+i+1)/2,
4489                                                         -(2*(f*u+d)*sqrt(z)+b)
4490                                                          ^2
4491                                                          /(4*(f*u+d)))
4492                                       *(2*(f*u+d)*sqrt(z)+b)
4493                                       +2
4494                                        *gamma_incomplete((j+i+2)/2,
4495                                                          -(2*(f*u+d)*sqrt(z)
4496                                                           +b)
4497                                                           ^2
4498                                                           /(4*(f*u+d)))
4499                                        *(f*u+d)
4500                                        *sqrt((2*(f*u+d)*sqrt(z)+b)^2/(f*u+d)))
4501                            /((2*(f*u+d)*sqrt(z)+b)^2/(-f*u-d))^((j+i+1)/2),i,
4502                           0,j),j,0,n))*(%e^(f*z+g))^u
4503           *%e^(-f*u*z-b^2/(4*(f*u+d))+e)
4504  /(f*u+d)^(2*(n+1))));
4505 0;
4506
4507 /* ----- Involving z^n*%e^(d*z)*(%e^(c*z^r))^u ------------------------------ */
4508
4509 /* Problem 668: NEW 9-1 */
4510 expand(niceindices(integrate(z^n*%e^(d*z)*(%e^(c*z^2))^u,z))-
4511 (-c^(-n-1)*u^(-n-1)*%e^(-z*(c*u*z+d)+d*z-d^2/(4*c*u))*(%e^(c*z^2))^u
4512          *('sum(d^(n-i)*gamma_incomplete((i+1)/2,-(2*c*u*z+d)^2/(4*c*u))
4513                        *(-1)^(i-n)*2^(i-n)*binomial(n,i)*(2*c*u*z+d)^(i+1)
4514                  /(-(2*c*u*z+d)^2/(c*u))^((i+1)/2),i,0,n))
4515  /2));
4516 0;
4517
4518 /* Problem 669: NEW 10-1 */
4519 expand(niceindices(integrate(z^n*%e^(d*z)*(%e^(c*sqrt(z)))^u,z))-
4520 (2^(-2*n-1)*('sum(4^j*binomial(n,j)
4521                     *'sum(c^(2*n-j-i)*(-1)^(i-j)*binomial(j,i)*u^(2*n-j-i)
4522                                      *(2*d*sqrt(z)+c*u)^(j+i)
4523                                      *(c
4524                                       *gamma_incomplete((j+i+1)/2,
4525                                                         -(2*d*sqrt(z)+c*u)^2
4526                                                          /(4*d))*u
4527                                       *(2*d*sqrt(z)+c*u)
4528                                       +2*d
4529                                         *gamma_incomplete((j+i+2)/2,
4530                                                           -(2*d*sqrt(z)+c*u)^2
4531                                                            /(4*d))
4532                                         *sqrt((2*d*sqrt(z)+c*u)^2/d))
4533                            /(-(2*d*sqrt(z)+c*u)^2/d)^((j+i+1)/2),i,0,j),j,0,
4534                  n))*(%e^(c*sqrt(z)))^u*%e^(-c*u*sqrt(z)-c^2*u^2/(4*d))
4535  /d^(2*(n+1))));
4536 0;
4537
4538 /* ----- Involving z^n*%e^(d*z+e)*(%e^(c*z^r))^u ---------------------------- */
4539
4540 /* Problem 670: NEW 9-1 */
4541 expand(niceindices(integrate(z^n*%e^(e+d*z)*(%e^(c*z^2))^u,z))-
4542 (-c^(-n-1)*u^(-n-1)*%e^(-z*(c*u*z+d)+d*z-d^2/(4*c*u)+e)*(%e^(c*z^2))^u
4543          *('sum(d^(n-i)*gamma_incomplete((i+1)/2,-(2*c*u*z+d)^2/(4*c*u))
4544                        *(-1)^(i-n)*2^(i-n)*binomial(n,i)*(2*c*u*z+d)^(i+1)
4545                  /(-(2*c*u*z+d)^2/(c*u))^((i+1)/2),i,0,n))
4546  /2));
4547 0;
4548
4549 /* Problem 671: NEW 10-1 */
4550 expand(niceindices(integrate(z^n*%e^(e+d*z)*(%e^(c*sqrt(z)))^u,z))-
4551 (2^(-2*n-1)*('sum(4^j*binomial(n,j)
4552                     *'sum(c^(2*n-j-i)*(-1)^(i-j)*binomial(j,i)*u^(2*n-j-i)
4553                                      *(2*d*sqrt(z)+c*u)^(j+i)
4554                                      *(c
4555                                       *gamma_incomplete((j+i+1)/2,
4556                                                         -(2*d*sqrt(z)+c*u)^2
4557                                                          /(4*d))*u
4558                                       *(2*d*sqrt(z)+c*u)
4559                                       +2*d
4560                                         *gamma_incomplete((j+i+2)/2,
4561                                                           -(2*d*sqrt(z)+c*u)^2
4562                                                            /(4*d))
4563                                         *sqrt((2*d*sqrt(z)+c*u)^2/d))
4564                            /(-(2*d*sqrt(z)+c*u)^2/d)^((j+i+1)/2),i,0,j),j,0,
4565                  n))*(%e^(c*sqrt(z)))^u*%e^(-c*u*sqrt(z)-c^2*u^2/(4*d)+e)
4566  /d^(2*(n+1))));
4567 0;
4568
4569 /* ----- Involving z^(v-1)*%e^(b*z^r)*(%e^(c*z^r))^u ------------------------ */
4570
4571 /* Problem 672: NEW 7-1*/
4572 diffcheck(integrate(z^(v-1)*%e^(b*z^r)*(%e^(c*z^r))^u,z),z,factor);
4573 z^(v-1)*%e^(b*z^r)*(%e^(c*z^r))^u;
4574
4575 /* Problem 673: NEW 7-1 */
4576 diffcheck(integrate(z^n*%e^(b*z^2)*(%e^(c*z^2))^u,z),z,factor);
4577 z^n*%e^(b*z^2)*(%e^(c*z^2))^u;
4578
4579 /* Problem 674: NEW 7-1 */
4580 diffcheck(integrate(z^(2*n)*%e^(b*z^2)*(%e^(c*z^2))^u,z),z,factor);
4581 z^(2*n)*%e^(b*z^2)*(%e^(c*z^2))^u;
4582
4583 /* Problem 675: NEW 7-1 */
4584 diffcheck(integrate(z^(1+2*n)*%e^(b*z^2)*(%e^(c*z^2))^u,z),z,factor);
4585 z^(1+2*n)*%e^(b*z^2)*(%e^(c*z^2))^u;
4586
4587 /* Problem 676: NEW 7-1 */
4588 diffcheck(integrate(z^n*%e^(b*sqrt(z))*(%e^(c*sqrt(z)))^u,z),z,factor);
4589 z^n*%e^(b*sqrt(z))*(%e^(c*sqrt(z)))^u;
4590
4591 /* ----- Involving z^(v-1)*%e^(b*z^r+e)*(%e^(c*z^r))^u ---------------------- */
4592
4593 /* Problem 677: NEW 7-1 */
4594 diffcheck(integrate(z^(v-1)*%e^(e+b*z^r)*(%e^(c*z^r))^u,z),z,factor);
4595 z^(v-1)*%e^(e+b*z^r)*(%e^(c*z^r))^u;
4596
4597 /* Problem 678: NEW 7-1 */
4598 diffcheck(integrate(z^n*%e^(e+b*z^2)*(%e^(c*z^2))^u,z),z,factor);
4599 z^n*%e^(e+b*z^2)*(%e^(c*z^2))^u;
4600
4601 /* Problem 679: NEW 7-1 */
4602 diffcheck(integrate(z^(2*n)*%e^(e+b*z^2)*(%e^(c*z^2))^u,z),z,factor);
4603 z^(2*n)*%e^(e+b*z^2)*(%e^(c*z^2))^u;
4604
4605 /* Problem 680: NEW 7-1 */
4606 diffcheck(integrate(z^(1+2*n)*%e^(e+b*z^2)*(%e^(c*z^2))^u,z),z,factor);
4607 z^(1+2*n)*%e^(e+b*z^2)*(%e^(c*z^2))^u;
4608
4609 /* Problem 681: NEW 7-1 */
4610 diffcheck(integrate(z^n*%e^(e+b*sqrt(z))*(%e^(c*sqrt(z)))^u,z),z,factor);
4611 z^n*%e^(e+b*sqrt(z))*(%e^(c*sqrt(z)))^u;
4612
4613 /* ----- Involving z^n*%e^(b*z^r+d*z)*(%e^(c*z^r))^u ------------------------ */
4614
4615 /* Problem 682: NEW 9-1 */
4616 expand(niceindices(integrate(z^n*%e^(d*z+b*z^2)*(%e^(c*z^2))^u,z))-
4617 (-(c*u+b)^(-n-1)*%e^(-z*(c*u*z+b*z+d)+z*(b*z+d)-d^2/(4*(c*u+b)))*(%e^(c*z^2))^u
4618                *('sum(d^(n-i)*gamma_incomplete((i+1)/2,
4619                                                -(2*(c*u+b)*z+d)^2/(4*(c*u+b)))
4620                              *(-1)^(i-n)*2^(i-n)*binomial(n,i)
4621                              *(2*(c*u+b)*z+d)^(i+1)
4622                        /((2*(c*u+b)*z+d)^2/(-c*u-b))^((i+1)/2),i,0,n))
4623  /2));
4624 0;
4625
4626 /* Problem 683: NEW 10-1 */
4627 expand(niceindices(integrate(z^n*%e^(d*z+b*sqrt(z))*(%e^(c*sqrt(z)))^u,z))-
4628 (2^(-2*n-1)*('sum(4^j*binomial(n,j)
4629                     *'sum((-1)^(i-j)*binomial(j,i)*(c*u+b)^(2*n-j-i)
4630                                     *(2*d*sqrt(z)+c*u+b)^(j+i)
4631                                     *(gamma_incomplete((j+i+1)/2,
4632                                                        -(2*d*sqrt(z)+c*u+b)^2
4633                                                         /(4*d))
4634                                      *(c*u+b)*(2*d*sqrt(z)+c*u+b)
4635                                      +2*d
4636                                        *gamma_incomplete((j+i+2)/2,
4637                                                          -(2*d*sqrt(z)+c*u+b)
4638                                                           ^2
4639                                                           /(4*d))
4640                                        *sqrt((2*d*sqrt(z)+c*u+b)^2/d))
4641                            /(-(2*d*sqrt(z)+c*u+b)^2/d)^((j+i+1)/2),i,0,j),j,0,
4642                  n))*(%e^(c*sqrt(z)))^u*%e^(-c*u*sqrt(z)-(c*u+b)^2/(4*d))
4643  /d^(2*(n+1))));
4644 0;
4645
4646 /* ----- Involving z^n*%e^(b*z^r+d*z+e)*(%e^(c*z^r))^u ---------------------- */
4647
4648 /* Problem 684: NEW 9-1 */
4649 expand(niceindices(integrate(z^n*%e^(e+d*z+b*z^2)*(%e^(c*z^2))^u,z))-
4650 (-(c*u+b)^(-n-1)*%e^(-z*(c*u*z+b*z+d)+z*(b*z+d)-d^2/(4*(c*u+b))+e)
4651                *(%e^(c*z^2))^u
4652                *('sum(d^(n-i)*gamma_incomplete((i+1)/2,
4653                                                -(2*(c*u+b)*z+d)^2/(4*(c*u+b)))
4654                              *(-1)^(i-n)*2^(i-n)*binomial(n,i)
4655                              *(2*(c*u+b)*z+d)^(i+1)
4656                        /((2*(c*u+b)*z+d)^2/(-c*u-b))^((i+1)/2),i,0,n))
4657  /2));
4658 0;
4659
4660 /* Problem 685: NEW 10-1 */
4661 expand(niceindices(integrate(z^n*%e^(e+d*z+b*sqrt(z))*(%e^(c*sqrt(z)))^u,z))-
4662 (2^(-2*n-1)*('sum(4^j*binomial(n,j)
4663                     *'sum((-1)^(i-j)*binomial(j,i)*(c*u+b)^(2*n-j-i)
4664                                     *(2*d*sqrt(z)+c*u+b)^(j+i)
4665                                     *(gamma_incomplete((j+i+1)/2,
4666                                                        -(2*d*sqrt(z)+c*u+b)^2
4667                                                         /(4*d))
4668                                      *(c*u+b)*(2*d*sqrt(z)+c*u+b)
4669                                      +2*d
4670                                        *gamma_incomplete((j+i+2)/2,
4671                                                          -(2*d*sqrt(z)+c*u+b)
4672                                                           ^2
4673                                                           /(4*d))
4674                                        *sqrt((2*d*sqrt(z)+c*u+b)^2/d))
4675                            /(-(2*d*sqrt(z)+c*u+b)^2/d)^((j+i+1)/2),i,0,j),j,0,
4676                  n))*(%e^(c*sqrt(z)))^u*%e^(-c*u*sqrt(z)-(c*u+b)^2/(4*d)+e)
4677  /d^(2*(n+1))));
4678 0;
4679
4680 /* ----- Involving z^n*%e^(d*z)*(%e^(c*z^r+g))^u ---------------------------- */
4681
4682 /* Problem 686: NEW 9-1 */
4683 expand(niceindices(integrate(z^n*%e^(d*z)*(%e^(g+c*z^2))^u,z))-
4684 (-c^(-n-1)*u^(-n-1)*%e^(-z*(c*u*z+d)+d*z-d^2/(4*c*u))*(%e^(c*z^2+g))^u
4685          *('sum(d^(n-i)*gamma_incomplete((i+1)/2,-(2*c*u*z+d)^2/(4*c*u))
4686                        *(-1)^(i-n)*2^(i-n)*binomial(n,i)*(2*c*u*z+d)^(i+1)
4687                  /(-(2*c*u*z+d)^2/(c*u))^((i+1)/2),i,0,n))
4688  /2));
4689 0;
4690
4691 /* Problem 687: NEW 10-1 */
4692 expand(niceindices(integrate(z^n*%e^(d*z)*(%e^(g+c*sqrt(z)))^u,z))-
4693 (2^(-2*n-1)*('sum(4^j*binomial(n,j)
4694                     *'sum(c^(2*n-j-i)*(-1)^(i-j)*binomial(j,i)*u^(2*n-j-i)
4695                                      *(2*d*sqrt(z)+c*u)^(j+i)
4696                                      *(c
4697                                       *gamma_incomplete((j+i+1)/2,
4698                                                         -(2*d*sqrt(z)+c*u)^2
4699                                                          /(4*d))*u
4700                                       *(2*d*sqrt(z)+c*u)
4701                                       +2*d
4702                                         *gamma_incomplete((j+i+2)/2,
4703                                                           -(2*d*sqrt(z)+c*u)^2
4704                                                            /(4*d))
4705                                         *sqrt((2*d*sqrt(z)+c*u)^2/d))
4706                            /(-(2*d*sqrt(z)+c*u)^2/d)^((j+i+1)/2),i,0,j),j,0,
4707                  n))*(%e^(c*sqrt(z)+g))^u*%e^(-c*u*sqrt(z)-c^2*u^2/(4*d))
4708  /d^(2*(n+1))));
4709 0;
4710
4711 /* ----- Involving z^n*%e^(d*z+e)*(%e^(c*z^r+g))^u -------------------------- */
4712
4713 /* Problem 688: NEW 9-1 */
4714 expand(niceindices(integrate(z^n*%e^(e+d*z)*(%e^(g+c*z^2))^u,z))-
4715 (-c^(-n-1)*u^(-n-1)*%e^(-z*(c*u*z+d)+d*z-d^2/(4*c*u)+e)*(%e^(c*z^2+g))^u
4716          *('sum(d^(n-i)*gamma_incomplete((i+1)/2,-(2*c*u*z+d)^2/(4*c*u))
4717                        *(-1)^(i-n)*2^(i-n)*binomial(n,i)*(2*c*u*z+d)^(i+1)
4718                  /(-(2*c*u*z+d)^2/(c*u))^((i+1)/2),i,0,n))
4719  /2));
4720 0;
4721
4722 /* Problem 689: NEW 10-1 */
4723 expand(niceindices(integrate(z^n*%e^(e+d*z)*(%e^(g+c*sqrt(z)))^u,z))-
4724 (2^(-2*n-1)*('sum(4^j*binomial(n,j)
4725                     *'sum(c^(2*n-j-i)*(-1)^(i-j)*binomial(j,i)*u^(2*n-j-i)
4726                                      *(2*d*sqrt(z)+c*u)^(j+i)
4727                                      *(c
4728                                       *gamma_incomplete((j+i+1)/2,
4729                                                         -(2*d*sqrt(z)+c*u)^2
4730                                                          /(4*d))*u
4731                                       *(2*d*sqrt(z)+c*u)
4732                                       +2*d
4733                                         *gamma_incomplete((j+i+2)/2,
4734                                                           -(2*d*sqrt(z)+c*u)^2
4735                                                            /(4*d))
4736                                         *sqrt((2*d*sqrt(z)+c*u)^2/d))
4737                            /(-(2*d*sqrt(z)+c*u)^2/d)^((j+i+1)/2),i,0,j),j,0,
4738                  n))*(%e^(c*sqrt(z)+g))^u*%e^(-c*u*sqrt(z)-c^2*u^2/(4*d)+e)
4739  /d^(2*(n+1))));
4740 0;
4741
4742 /* ----- Involving z^(v-1)*%e^(b*z^r)*(%e^(c*z^r+g))^u ---------------------- */
4743
4744 /* Problem 690: NEW 7-1 */
4745 diffcheck(integrate(z^(v-1)*%e^(b*z^r)*(%e^(g+c*z^r))^u,z),z,factor);
4746 z^(v-1)*%e^(b*z^r)*(%e^(g+c*z^r))^u;
4747
4748 /* Problem 691: NEW 7-1 */
4749 diffcheck(integrate(z^n*%e^(b*z^2)*(%e^(g+c*z^2))^u,z),z,factor);
4750 z^n*%e^(b*z^2)*(%e^(g+c*z^2))^u;
4751
4752 /* Problem 692: NEW 7-1 */
4753 diffcheck(integrate(z^(2*n)*%e^(b*z^2)*(%e^(g+c*z^2))^u,z),z,factor);
4754 z^(2*n)*%e^(b*z^2)*(%e^(g+c*z^2))^u;
4755
4756 /* Problem 693: NEW 7-1 */
4757 diffcheck(integrate(z^(1+2*n)*%e^(b*z^2)*(%e^(g+c*z^2))^u,z),z,factor);
4758 z^(1+2*n)*%e^(b*z^2)*(%e^(g+c*z^2))^u;
4759
4760 /* Problem 694: NEW 7-1*/
4761 diffcheck(integrate(z^n*%e^(b*sqrt(z))*(%e^(g+c*sqrt(z)))^u,z),z,factor);
4762 z^n*%e^(b*sqrt(z))*(%e^(g+c*sqrt(z)))^u;
4763
4764 /* ----- Involving z^(v-1)*%e^(b*z^r+e)*(%e^(c*z^r+g))^u -------------------- */
4765
4766 /* Problem 695: NEW 7-1 */
4767 diffcheck(integrate(z^(v-1)*%e^(e+b*z^r)*(%e^(g+c*z^r))^u,z),z,factor);
4768 z^(v-1)*%e^(e+b*z^r)*(%e^(g+c*z^r))^u;
4769
4770 /* Problem 696: NEW 7-1 */
4771 diffcheck(integrate(z^n*%e^(e+b*z^2)*(%e^(g+c*z^2))^u,z),z,factor);
4772 z^n*%e^(e+b*z^2)*(%e^(g+c*z^2))^u;
4773
4774 /* Problem 697: NEW 7-1 */
4775 diffcheck(integrate(z^(2*n)*%e^(e+b*z^2)*(%e^(g+c*z^2))^u,z),z,factor);
4776 z^(2*n)*%e^(e+b*z^2)*(%e^(g+c*z^2))^u;
4777
4778 /* Problem 698: NEW 7-1 */
4779 diffcheck(integrate(z^(1+2*n)*%e^(e+b*z^2)*(%e^(g+c*z^2))^u,z),z,factor);
4780 z^(1+2*n)*%e^(e+b*z^2)*(%e^(g+c*z^2))^u;
4781
4782 /* Problem 699: NEW 7-1 */
4783 diffcheck(integrate(z^n*%e^(e+b*sqrt(z))*(%e^(g+c*sqrt(z)))^u,z),z,factor);
4784 z^n*%e^(e+b*sqrt(z))*(%e^(g+c*sqrt(z)))^u;
4785
4786 /* ----- Involving z^n*%e^(b*z^r+d*z)*(%e^(c*z^r+g))^u ---------------------- */
4787
4788 /* Problem 700: NEW 9-1 */
4789 expand(niceindices(integrate(z^n*%e^(d*z+b*z^2)*(%e^(g+c*z^2))^u,z))-
4790 (-(c*u+b)^(-n-1)*%e^(-z*(c*u*z+b*z+d)+z*(b*z+d)-d^2/(4*(c*u+b)))
4791                *(%e^(c*z^2+g))^u
4792                *('sum(d^(n-i)*gamma_incomplete((i+1)/2,
4793                                                -(2*(c*u+b)*z+d)^2/(4*(c*u+b)))
4794                              *(-1)^(i-n)*2^(i-n)*binomial(n,i)
4795                              *(2*(c*u+b)*z+d)^(i+1)
4796                        /((2*(c*u+b)*z+d)^2/(-c*u-b))^((i+1)/2),i,0,n))
4797  /2));
4798 0;
4799
4800 /* Problem 701: NEW 10-1 */
4801 expand(niceindices(integrate(z^n*%e^(d*z+b*sqrt(z))*(%e^(g+c*sqrt(z)))^u,z))-
4802 (2^(-2*n-1)*('sum(4^j*binomial(n,j)
4803                     *'sum((-1)^(i-j)*binomial(j,i)*(c*u+b)^(2*n-j-i)
4804                                     *(2*d*sqrt(z)+c*u+b)^(j+i)
4805                                     *(gamma_incomplete((j+i+1)/2,
4806                                                        -(2*d*sqrt(z)+c*u+b)^2
4807                                                         /(4*d))
4808                                      *(c*u+b)*(2*d*sqrt(z)+c*u+b)
4809                                      +2*d
4810                                        *gamma_incomplete((j+i+2)/2,
4811                                                          -(2*d*sqrt(z)+c*u+b)
4812                                                           ^2
4813                                                           /(4*d))
4814                                        *sqrt((2*d*sqrt(z)+c*u+b)^2/d))
4815                            /(-(2*d*sqrt(z)+c*u+b)^2/d)^((j+i+1)/2),i,0,j),j,0,
4816                  n))*(%e^(c*sqrt(z)+g))^u*%e^(-c*u*sqrt(z)-(c*u+b)^2/(4*d))
4817  /d^(2*(n+1))));
4818 0;
4819
4820 /* ----- Involving z^n*%e^(b*z^r+d*z+e)*(%e^(c*z^r+g))^u -------------------- */
4821
4822 /* Problem 702: NEW 9-1 */
4823 expand(niceindices(integrate(z^n*%e^(e+d*z+b*z^2)*(%e^(g+c*z^2))^u,z))-
4824 (-(c*u+b)^(-n-1)*%e^(-z*(c*u*z+b*z+d)+z*(b*z+d)-d^2/(4*(c*u+b))+e)
4825                *(%e^(c*z^2+g))^u
4826                *('sum(d^(n-i)*gamma_incomplete((i+1)/2,
4827                                                -(2*(c*u+b)*z+d)^2/(4*(c*u+b)))
4828                              *(-1)^(i-n)*2^(i-n)*binomial(n,i)
4829                              *(2*(c*u+b)*z+d)^(i+1)
4830                        /((2*(c*u+b)*z+d)^2/(-c*u-b))^((i+1)/2),i,0,n))
4831  /2));
4832 0;
4833
4834 /* Problem 703: NEW 10-1 */
4835 expand(niceindices(integrate(z^n*%e^(e+d*z+b*sqrt(z))*(%e^(g+c*sqrt(z)))^u,z))-
4836 (2^(-2*n-1)*('sum(4^j*binomial(n,j)
4837                     *'sum((-1)^(i-j)*binomial(j,i)*(c*u+b)^(2*n-j-i)
4838                                     *(2*d*sqrt(z)+c*u+b)^(j+i)
4839                                     *(gamma_incomplete((j+i+1)/2,
4840                                                        -(2*d*sqrt(z)+c*u+b)^2
4841                                                         /(4*d))
4842                                      *(c*u+b)*(2*d*sqrt(z)+c*u+b)
4843                                      +2*d
4844                                        *gamma_incomplete((j+i+2)/2,
4845                                                          -(2*d*sqrt(z)+c*u+b)
4846                                                           ^2
4847                                                           /(4*d))
4848                                        *sqrt((2*d*sqrt(z)+c*u+b)^2/d))
4849                            /(-(2*d*sqrt(z)+c*u+b)^2/d)^((j+i+1)/2),i,0,j),j,0,
4850                  n))*(%e^(c*sqrt(z)+g))^u*%e^(-c*u*sqrt(z)-(c*u+b)^2/(4*d)+e)
4851  /d^(2*(n+1))));
4852  0;
4853
4854 /* ----- Involving z^n*%e^(d*z)*(%e^(c*z^r+f*z))^u -------------------------- */
4855
4856 /* Problem 704: NEW 9-1 */
4857 expand(niceindices(integrate(z^n*%e^(d*z)*(%e^(f*z+c*z^2))^u,z))-
4858 (-c^(-n-1)*u^(-n-1)*(%e^(z*(c*z+f)))^u
4859          *%e^(-z*(c*u*z+f*u+d)+d*z-(f*u+d)^2/(4*c*u))
4860          *('sum(gamma_incomplete((i+1)/2,-(2*c*u*z+f*u+d)^2/(4*c*u))
4861                  *2^(i-n)*binomial(n,i)*(-f*u-d)^(n-i)*(2*c*u*z+f*u+d)^(i+1)
4862                  /(-(2*c*u*z+f*u+d)^2/(c*u))^((i+1)/2),i,0,n))
4863  /2));
4864 0;
4865
4866 /* Problem 705: NEW 10-1 */
4867 expand(niceindices(integrate(z^n*%e^(d*z)*(%e^(f*z+c*sqrt(z)))^u,z))-
4868 (2^(-2*n-1)*('sum(4^j*binomial(n,j)
4869                     *'sum(c^(2*n-j-i)*(-1)^(i-j)*binomial(j,i)*u^(2*n-j-i)
4870                                      *(2*(f*u+d)*sqrt(z)+c*u)^(j+i)
4871                                      *(c
4872                                       *gamma_incomplete((j+i+1)/2,
4873                                                         -(2*(f*u+d)*sqrt(z)
4874                                                          +c*u)
4875                                                          ^2
4876                                                          /(4*(f*u+d)))*u
4877                                       *(2*(f*u+d)*sqrt(z)+c*u)
4878                                       +2
4879                                        *gamma_incomplete((j+i+2)/2,
4880                                                          -(2*(f*u+d)*sqrt(z)
4881                                                           +c*u)
4882                                                           ^2
4883                                                           /(4*(f*u+d)))
4884                                        *(f*u+d)
4885                                        *sqrt(
4886                                         (2*(f*u+d)*sqrt(z)+c*u)^2/(f*u+d)))
4887                            /((2*(f*u+d)*sqrt(z)+c*u)^2/(-f*u-d))^((j+i+1)/2),
4888                           i,0,j),j,0,n))*(%e^(f*z+c*sqrt(z)))^u
4889           *%e^(-f*u*z-c*u*sqrt(z)-c^2*u^2/(4*(f*u+d)))
4890  /(f*u+d)^(2*(n+1))));
4891 0;
4892
4893 /* ----- Involving z^n*%e^(d*z+e)*(%e^(c*z^r+f*z))^u ------------------------ */
4894
4895 /* Problem 706: NEW 9-1 */
4896 expand(niceindices(integrate(z^n*%e^(e+d*z)*(%e^(f*z+c*z^2))^u,z))-
4897 (-c^(-n-1)*u^(-n-1)*(%e^(z*(c*z+f)))^u
4898          *%e^(-z*(c*u*z+f*u+d)+d*z-(f*u+d)^2/(4*c*u)+e)
4899          *('sum(gamma_incomplete((i+1)/2,-(2*c*u*z+f*u+d)^2/(4*c*u))
4900                  *2^(i-n)*binomial(n,i)*(-f*u-d)^(n-i)*(2*c*u*z+f*u+d)^(i+1)
4901                  /(-(2*c*u*z+f*u+d)^2/(c*u))^((i+1)/2),i,0,n))
4902  /2));
4903 0;
4904
4905 /* Problem 707: NEW 10-1 */
4906 expand(niceindices(integrate(z^n*%e^(e+d*z)*(%e^(f*z+c*sqrt(z)))^u,z))-
4907 (2^(-2*n-1)*('sum(4^j*binomial(n,j)
4908                     *'sum(c^(2*n-j-i)*(-1)^(i-j)*binomial(j,i)*u^(2*n-j-i)
4909                                      *(2*(f*u+d)*sqrt(z)+c*u)^(j+i)
4910                                      *(c
4911                                       *gamma_incomplete((j+i+1)/2,
4912                                                         -(2*(f*u+d)*sqrt(z)
4913                                                          +c*u)
4914                                                          ^2
4915                                                          /(4*(f*u+d)))*u
4916                                       *(2*(f*u+d)*sqrt(z)+c*u)
4917                                       +2
4918                                        *gamma_incomplete((j+i+2)/2,
4919                                                          -(2*(f*u+d)*sqrt(z)
4920                                                           +c*u)
4921                                                           ^2
4922                                                           /(4*(f*u+d)))
4923                                        *(f*u+d)
4924                                        *sqrt(
4925                                         (2*(f*u+d)*sqrt(z)+c*u)^2/(f*u+d)))
4926                            /((2*(f*u+d)*sqrt(z)+c*u)^2/(-f*u-d))^((j+i+1)/2),
4927                           i,0,j),j,0,n))*(%e^(f*z+c*sqrt(z)))^u
4928           *%e^(-f*u*z-c*u*sqrt(z)-c^2*u^2/(4*(f*u+d))+e)
4929  /(f*u+d)^(2*(n+1))));
4930 0;
4931
4932 /* ----- Involving z^n*%e^(b*z^r)*(%e^(c*z^r+f*z))^u ------------------------ */
4933
4934 /* Problem 708: NEW 9-1 */
4935 expand(niceindices(integrate(z^n*%e^(b*z^2)*(%e^(f*z+c*z^2))^u,z))-
4936 (-(c*u+b)^(-n-1)*(%e^(z*(c*z+f)))^u
4937                *%e^(b*z^2-z*(c*u*z+b*z+f*u)-f^2*u^2/(4*(c*u+b)))
4938                *('sum(f^(n-i)*gamma_incomplete((i+1)/2,
4939                                                -(2*(c*u+b)*z+f*u)^2
4940                                                 /(4*(c*u+b)))*(-1)^(i-n)
4941                              *2^(i-n)*binomial(n,i)*u^(n-i)
4942                              *(2*(c*u+b)*z+f*u)^(i+1)
4943                        /((2*(c*u+b)*z+f*u)^2/(-c*u-b))^((i+1)/2),i,0,n))
4944  /2));
4945 0;
4946
4947 /* Problem 709: NEW 10-1 */
4948 expand(niceindices(integrate(z^n*%e^(b*sqrt(z))*(%e^(f*z+c*sqrt(z)))^u,z))-
4949 (2^(-2*n-1)*('sum(4^j*binomial(n,j)
4950                     *'sum((-1)^(i-j)*binomial(j,i)*(c*u+b)^(2*n-j-i)
4951                                     *(2*f*u*sqrt(z)+c*u+b)^(j+i)
4952                                     *(gamma_incomplete((j+i+1)/2,
4953                                                        -(2*f*u*sqrt(z)+c*u+b)
4954                                                         ^2
4955                                                         /(4*f*u))
4956                                      *(c*u+b)*(2*f*u*sqrt(z)+c*u+b)
4957                                      +2*f
4958                                        *gamma_incomplete((j+i+2)/2,
4959                                                          -(2*f*u*sqrt(z)
4960                                                           +c*u+b)
4961                                                           ^2
4962                                                           /(4*f*u))*u
4963                                        *sqrt((2*f*u*sqrt(z)+c*u+b)^2/(f*u)))
4964                            /(-(2*f*u*sqrt(z)+c*u+b)^2/(f*u))^((j+i+1)/2),i,0,
4965                           j),j,0,n))*(%e^(f*z+c*sqrt(z)))^u
4966           *%e^(-f*u*z-c*u*sqrt(z)-(c*u+b)^2/(4*f*u))
4967  /(f^(2*(n+1))*u^(2*(n+1)))));
4968 0;
4969
4970 /* ----- Involving z^n*%e^(b*z^r+e)*(%e^(c*z^r+f*z))^u ---------------------- */
4971
4972 /* Problem 710: NEW 9-1 */
4973 expand(niceindices(integrate(z^n*%e^(e+b*z^2)*(%e^(f*z+c*z^2))^u,z))-
4974 (-(c*u+b)^(-n-1)*(%e^(z*(c*z+f)))^u
4975                *%e^(b*z^2-z*(c*u*z+b*z+f*u)-f^2*u^2/(4*(c*u+b))+e)
4976                *('sum(f^(n-i)*gamma_incomplete((i+1)/2,
4977                                                -(2*(c*u+b)*z+f*u)^2
4978                                                 /(4*(c*u+b)))*(-1)^(i-n)
4979                              *2^(i-n)*binomial(n,i)*u^(n-i)
4980                              *(2*(c*u+b)*z+f*u)^(i+1)
4981                        /((2*(c*u+b)*z+f*u)^2/(-c*u-b))^((i+1)/2),i,0,n))
4982  /2));
4983 0;
4984
4985 /* Problem 711: NEW 10-1 */
4986 expand(niceindices(integrate(z^n*%e^(e+b*sqrt(z))*(%e^(f*z+c*sqrt(z)))^u,z))-
4987 (2^(-2*n-1)*('sum(4^j*binomial(n,j)
4988                     *'sum((-1)^(i-j)*binomial(j,i)*(c*u+b)^(2*n-j-i)
4989                                     *(2*f*u*sqrt(z)+c*u+b)^(j+i)
4990                                     *(gamma_incomplete((j+i+1)/2,
4991                                                        -(2*f*u*sqrt(z)+c*u+b)
4992                                                         ^2
4993                                                         /(4*f*u))
4994                                      *(c*u+b)*(2*f*u*sqrt(z)+c*u+b)
4995                                      +2*f
4996                                        *gamma_incomplete((j+i+2)/2,
4997                                                          -(2*f*u*sqrt(z)
4998                                                           +c*u+b)
4999                                                           ^2
5000                                                           /(4*f*u))*u
5001                                        *sqrt((2*f*u*sqrt(z)+c*u+b)^2/(f*u)))
5002                            /(-(2*f*u*sqrt(z)+c*u+b)^2/(f*u))^((j+i+1)/2),i,0,
5003                           j),j,0,n))*(%e^(f*z+c*sqrt(z)))^u
5004           *%e^(-f*u*z-c*u*sqrt(z)-(c*u+b)^2/(4*f*u)+e)
5005  /(f^(2*(n+1))*u^(2*(n+1)))));
5006 0;
5007
5008 /* ----- Involving z^n*%e^(b*z^r+d*z)*(%e^(c*z^r+f*z))^u -------------------- */
5009
5010 /* Problem 712: NEW 9-1 */
5011 expand(niceindices(integrate(z^n*%e^(d*z+b*z^2)*(%e^(f*z+c*z^2))^u,z))-
5012 (-(c*u+b)^(-n-1)*(%e^(z*(c*z+f)))^u
5013                *%e^(-z*(c*u*z+b*z+f*u+d)+z*(b*z+d)-(f*u+d)^2/(4*(c*u+b)))
5014                *('sum(gamma_incomplete((i+1)/2,
5015                                        -(2*(c*u+b)*z+f*u+d)^2/(4*(c*u+b)))
5016                        *2^(i-n)*binomial(n,i)*(-f*u-d)^(n-i)
5017                        *(2*(c*u+b)*z+f*u+d)^(i+1)
5018                        /((2*(c*u+b)*z+f*u+d)^2/(-c*u-b))^((i+1)/2),i,0,n))
5019  /2));
5020 0;
5021
5022 /* Problem 713: NEW 10-1 */
5023 expand(niceindices(integrate(z^n*%e^(d*z+b*sqrt(z))*(%e^(f*z+c*sqrt(z)))^u,z))-
5024 (2^(-2*n-1)*('sum(4^j*binomial(n,j)
5025                     *'sum((-1)^(i-j)*binomial(j,i)*(c*u+b)^(2*n-j-i)
5026                                     *(2*(f*u+d)*sqrt(z)+c*u+b)^(j+i)
5027                                     *(gamma_incomplete((j+i+1)/2,
5028                                                        -(2*(f*u+d)*sqrt(z)
5029                                                         +c*u+b)
5030                                                         ^2
5031                                                         /(4*(f*u+d)))
5032                                      *(c*u+b)*(2*(f*u+d)*sqrt(z)+c*u+b)
5033                                      +2*gamma_incomplete((j+i+2)/2,
5034                                                          -(2*(f*u+d)*sqrt(z)
5035                                                           +c*u+b)
5036                                                           ^2
5037                                                           /(4*(f*u+d)))
5038                                        *(f*u+d)
5039                                        *sqrt(
5040                                         (2*(f*u+d)*sqrt(z)+c*u+b)^2/(f*u+d)))
5041                            /((2*(f*u+d)*sqrt(z)+c*u+b)^2/(-f*u-d))
5042                             ^((j+i+1)/2),i,0,j),j,0,n))*(%e^(f*z+c*sqrt(z)))^u
5043           *%e^(-f*u*z-c*u*sqrt(z)-(c*u+b)^2/(4*(f*u+d)))
5044  /(f*u+d)^(2*(n+1))));
5045 0;
5046
5047 /* ----- Involving z^n*%e^(b*z^r+d*z+e)*(%e^(c*z^r+f*z))^u ------------------ */
5048
5049 /* Problem 714: NEW 9-1 */
5050 expand(niceindices(integrate(z^n*%e^(e+d*z+b*z^2)*(%e^(f*z+c*z^2))^u,z))-
5051 (-(c*u+b)^(-n-1)*(%e^(z*(c*z+f)))^u
5052                *%e^(-z*(c*u*z+b*z+f*u+d)+z*(b*z+d)-(f*u+d)^2/(4*(c*u+b))+e)
5053                *('sum(gamma_incomplete((i+1)/2,
5054                                        -(2*(c*u+b)*z+f*u+d)^2/(4*(c*u+b)))
5055                        *2^(i-n)*binomial(n,i)*(-f*u-d)^(n-i)
5056                        *(2*(c*u+b)*z+f*u+d)^(i+1)
5057                        /((2*(c*u+b)*z+f*u+d)^2/(-c*u-b))^((i+1)/2),i,0,n))
5058  /2));
5059 0;
5060
5061 /* Problem 715: NEW 10-1 */
5062 expand(niceindices(integrate(z^n*%e^(e+d*z+b*sqrt(z))*(%e^(f*z+c*sqrt(z)))^u,z))-
5063 (2^(-2*n-1)*('sum(4^j*binomial(n,j)
5064                     *'sum((-1)^(i-j)*binomial(j,i)*(c*u+b)^(2*n-j-i)
5065                                     *(2*(f*u+d)*sqrt(z)+c*u+b)^(j+i)
5066                                     *(gamma_incomplete((j+i+1)/2,
5067                                                        -(2*(f*u+d)*sqrt(z)
5068                                                         +c*u+b)
5069                                                         ^2
5070                                                         /(4*(f*u+d)))
5071                                      *(c*u+b)*(2*(f*u+d)*sqrt(z)+c*u+b)
5072                                      +2*gamma_incomplete((j+i+2)/2,
5073                                                          -(2*(f*u+d)*sqrt(z)
5074                                                           +c*u+b)
5075                                                           ^2
5076                                                           /(4*(f*u+d)))
5077                                        *(f*u+d)
5078                                        *sqrt(
5079                                         (2*(f*u+d)*sqrt(z)+c*u+b)^2/(f*u+d)))
5080                            /((2*(f*u+d)*sqrt(z)+c*u+b)^2/(-f*u-d))
5081                             ^((j+i+1)/2),i,0,j),j,0,n))*(%e^(f*z+c*sqrt(z)))^u
5082           *%e^(-f*u*z-c*u*sqrt(z)-(c*u+b)^2/(4*(f*u+d))+e)
5083  /(f*u+d)^(2*(n+1))));
5084 0;
5085
5086 /* ----- Involving z^n*%e^(d*z)*(%e^(c*z^r+f*z+g))^u ------------------------ */
5087
5088 /* Problem 716: NEW 9-1 */
5089 expand(niceindices(integrate(z^n*%e^(d*z)*(%e^(g+f*z+c*z^2))^u,z))-
5090 (-c^(-n-1)*u^(-n-1)*(%e^(z*(c*z+f)+g))^u
5091          *%e^(-z*(c*u*z+f*u+d)+d*z-(f*u+d)^2/(4*c*u))
5092          *('sum(gamma_incomplete((i+1)/2,-(2*c*u*z+f*u+d)^2/(4*c*u))
5093                  *2^(i-n)*binomial(n,i)*(-f*u-d)^(n-i)*(2*c*u*z+f*u+d)^(i+1)
5094                  /(-(2*c*u*z+f*u+d)^2/(c*u))^((i+1)/2),i,0,n))
5095  /2));
5096 0;
5097
5098 /* Problem 717: NEW 10-1 */
5099 expand(niceindices(integrate(z^n*%e^(d*z)*(%e^(g+f*z+c*sqrt(z)))^u,z))-
5100 (2^(-2*n-1)*('sum(4^j*binomial(n,j)
5101                     *'sum(c^(2*n-j-i)*(-1)^(i-j)*binomial(j,i)*u^(2*n-j-i)
5102                                      *(2*(f*u+d)*sqrt(z)+c*u)^(j+i)
5103                                      *(c
5104                                       *gamma_incomplete((j+i+1)/2,
5105                                                         -(2*(f*u+d)*sqrt(z)
5106                                                          +c*u)
5107                                                          ^2
5108                                                          /(4*(f*u+d)))*u
5109                                       *(2*(f*u+d)*sqrt(z)+c*u)
5110                                       +2
5111                                        *gamma_incomplete((j+i+2)/2,
5112                                                          -(2*(f*u+d)*sqrt(z)
5113                                                           +c*u)
5114                                                           ^2
5115                                                           /(4*(f*u+d)))
5116                                        *(f*u+d)
5117                                        *sqrt(
5118                                         (2*(f*u+d)*sqrt(z)+c*u)^2/(f*u+d)))
5119                            /((2*(f*u+d)*sqrt(z)+c*u)^2/(-f*u-d))^((j+i+1)/2),
5120                           i,0,j),j,0,n))*(%e^(f*z+c*sqrt(z)+g))^u
5121           *%e^(-f*u*z-c*u*sqrt(z)-c^2*u^2/(4*(f*u+d)))
5122  /(f*u+d)^(2*(n+1))));
5123 0;
5124
5125 /* ----- Involving z^n*%e^(d*z+e)*(%e^(c*z^r+f*z+g))^u ---------------------- */
5126
5127 /* Problem 718: NEW 9-1 */
5128 expand(niceindices(integrate(z^n*%e^(e+d*z)*(%e^(g+f*z+c*z^2))^u,z))-
5129 (-c^(-n-1)*u^(-n-1)*(%e^(z*(c*z+f)+g))^u
5130          *%e^(-z*(c*u*z+f*u+d)+d*z-(f*u+d)^2/(4*c*u)+e)
5131          *('sum(gamma_incomplete((i+1)/2,-(2*c*u*z+f*u+d)^2/(4*c*u))
5132                  *2^(i-n)*binomial(n,i)*(-f*u-d)^(n-i)*(2*c*u*z+f*u+d)^(i+1)
5133                  /(-(2*c*u*z+f*u+d)^2/(c*u))^((i+1)/2),i,0,n))
5134  /2));
5135 0;
5136
5137 /* Problem 719: NEW 10-1 */
5138 expand(niceindices(integrate(z^n*%e^(e+d*z)*(%e^(g+f*z+c*sqrt(z)))^u,z))-
5139 (2^(-2*n-1)*('sum(4^j*binomial(n,j)
5140                     *'sum(c^(2*n-j-i)*(-1)^(i-j)*binomial(j,i)*u^(2*n-j-i)
5141                                      *(2*(f*u+d)*sqrt(z)+c*u)^(j+i)
5142                                      *(c
5143                                       *gamma_incomplete((j+i+1)/2,
5144                                                         -(2*(f*u+d)*sqrt(z)
5145                                                          +c*u)
5146                                                          ^2
5147                                                          /(4*(f*u+d)))*u
5148                                       *(2*(f*u+d)*sqrt(z)+c*u)
5149                                       +2
5150                                        *gamma_incomplete((j+i+2)/2,
5151                                                          -(2*(f*u+d)*sqrt(z)
5152                                                           +c*u)
5153                                                           ^2
5154                                                           /(4*(f*u+d)))
5155                                        *(f*u+d)
5156                                        *sqrt(
5157                                         (2*(f*u+d)*sqrt(z)+c*u)^2/(f*u+d)))
5158                            /((2*(f*u+d)*sqrt(z)+c*u)^2/(-f*u-d))^((j+i+1)/2),
5159                           i,0,j),j,0,n))*(%e^(f*z+c*sqrt(z)+g))^u
5160           *%e^(-f*u*z-c*u*sqrt(z)-c^2*u^2/(4*(f*u+d))+e)
5161  /(f*u+d)^(2*(n+1))));
5162 0;
5163
5164 /* ----- Involving z^n*%e^(b*z^r)*(%e^(c*z^r+f*z+g))^u ---------------------- */
5165
5166 /* Problem 720: NEW 9-1 */
5167 expand(niceindices(integrate(z^n*%e^(b*z^2)*(%e^(g+f*z+c*z^2))^u,z))-
5168 (-(c*u+b)^(-n-1)*(%e^(z*(c*z+f)+g))^u
5169                *%e^(b*z^2-z*(c*u*z+b*z+f*u)-f^2*u^2/(4*(c*u+b)))
5170                *('sum(f^(n-i)*gamma_incomplete((i+1)/2,
5171                                                -(2*(c*u+b)*z+f*u)^2
5172                                                 /(4*(c*u+b)))*(-1)^(i-n)
5173                              *2^(i-n)*binomial(n,i)*u^(n-i)
5174                              *(2*(c*u+b)*z+f*u)^(i+1)
5175                        /((2*(c*u+b)*z+f*u)^2/(-c*u-b))^((i+1)/2),i,0,n))
5176  /2));
5177 0;
5178
5179 /* Problem 721: NEW 10-1 */
5180 expand(niceindices(integrate(z^n*%e^(b*sqrt(z))*(%e^(g+f*z+c*sqrt(z)))^u,z))-
5181 (2^(-2*n-1)*('sum(4^j*binomial(n,j)
5182                     *'sum((-1)^(i-j)*binomial(j,i)*(c*u+b)^(2*n-j-i)
5183                                     *(2*f*u*sqrt(z)+c*u+b)^(j+i)
5184                                     *(gamma_incomplete((j+i+1)/2,
5185                                                        -(2*f*u*sqrt(z)+c*u+b)
5186                                                         ^2
5187                                                         /(4*f*u))
5188                                      *(c*u+b)*(2*f*u*sqrt(z)+c*u+b)
5189                                      +2*f
5190                                        *gamma_incomplete((j+i+2)/2,
5191                                                          -(2*f*u*sqrt(z)
5192                                                           +c*u+b)
5193                                                           ^2
5194                                                           /(4*f*u))*u
5195                                        *sqrt((2*f*u*sqrt(z)+c*u+b)^2/(f*u)))
5196                            /(-(2*f*u*sqrt(z)+c*u+b)^2/(f*u))^((j+i+1)/2),i,0,
5197                           j),j,0,n))*(%e^(f*z+c*sqrt(z)+g))^u
5198           *%e^(-f*u*z-c*u*sqrt(z)-(c*u+b)^2/(4*f*u))
5199  /(f^(2*(n+1))*u^(2*(n+1)))));
5200 0;
5201
5202 /* ----- Involving z^n*%e^(b*z^r+e)*(%e^(c*z^r+f*z+g))^u -------------------- */
5203
5204 /* Problem 722: NEW 9-1 */
5205 expand(niceindices(integrate(z^n*%e^(e+b*z^2)*(%e^(g+f*z+c*z^2))^u,z))-
5206 (-(c*u+b)^(-n-1)*(%e^(z*(c*z+f)+g))^u
5207                *%e^(b*z^2-z*(c*u*z+b*z+f*u)-f^2*u^2/(4*(c*u+b))+e)
5208                *('sum(f^(n-i)*gamma_incomplete((i+1)/2,
5209                                                -(2*(c*u+b)*z+f*u)^2
5210                                                 /(4*(c*u+b)))*(-1)^(i-n)
5211                              *2^(i-n)*binomial(n,i)*u^(n-i)
5212                              *(2*(c*u+b)*z+f*u)^(i+1)
5213                        /((2*(c*u+b)*z+f*u)^2/(-c*u-b))^((i+1)/2),i,0,n))
5214  /2));
5215  0;
5216
5217 /* Problem 723: NEW 10-1 */
5218 expand(niceindices(integrate(z^n*%e^(e+b*sqrt(z))*(%e^(g+f*z+c*sqrt(z)))^u,z))-
5219 (2^(-2*n-1)*('sum(4^j*binomial(n,j)
5220                     *'sum((-1)^(i-j)*binomial(j,i)*(c*u+b)^(2*n-j-i)
5221                                     *(2*f*u*sqrt(z)+c*u+b)^(j+i)
5222                                     *(gamma_incomplete((j+i+1)/2,
5223                                                        -(2*f*u*sqrt(z)+c*u+b)
5224                                                         ^2
5225                                                         /(4*f*u))
5226                                      *(c*u+b)*(2*f*u*sqrt(z)+c*u+b)
5227                                      +2*f
5228                                        *gamma_incomplete((j+i+2)/2,
5229                                                          -(2*f*u*sqrt(z)
5230                                                           +c*u+b)
5231                                                           ^2
5232                                                           /(4*f*u))*u
5233                                        *sqrt((2*f*u*sqrt(z)+c*u+b)^2/(f*u)))
5234                            /(-(2*f*u*sqrt(z)+c*u+b)^2/(f*u))^((j+i+1)/2),i,0,
5235                           j),j,0,n))*(%e^(f*z+c*sqrt(z)+g))^u
5236           *%e^(-f*u*z-c*u*sqrt(z)-(c*u+b)^2/(4*f*u)+e)
5237  /(f^(2*(n+1))*u^(2*(n+1)))));
5238 0;
5239
5240 /* ----- Involving z^n*%e^(b*z^r+d*z)*(%e^(c*z^r+f*z+g))^u ------------------ */
5241
5242 /* Problem 724: NEW 9-1 */
5243 expand(niceindices(integrate(z^n*%e^(d*z+b*z^2)*(%e^(g+f*z+c*z^2))^u,z))-
5244 (-(c*u+b)^(-n-1)*(%e^(z*(c*z+f)+g))^u
5245                *%e^(-z*(c*u*z+b*z+f*u+d)+z*(b*z+d)-(f*u+d)^2/(4*(c*u+b)))
5246                *('sum(gamma_incomplete((i+1)/2,
5247                                        -(2*(c*u+b)*z+f*u+d)^2/(4*(c*u+b)))
5248                        *2^(i-n)*binomial(n,i)*(-f*u-d)^(n-i)
5249                        *(2*(c*u+b)*z+f*u+d)^(i+1)
5250                        /((2*(c*u+b)*z+f*u+d)^2/(-c*u-b))^((i+1)/2),i,0,n))
5251  /2));
5252 0;
5253
5254 /* Problem 725: NEW 10-1 */
5255 expand(niceindices(integrate(z^n*%e^(d*z+b*sqrt(z))*(%e^(g+f*z+c*sqrt(z)))^u,z))-
5256 (2^(-2*n-1)*('sum(4^j*binomial(n,j)
5257                     *'sum((-1)^(i-j)*binomial(j,i)*(c*u+b)^(2*n-j-i)
5258                                     *(2*(f*u+d)*sqrt(z)+c*u+b)^(j+i)
5259                                     *(gamma_incomplete((j+i+1)/2,
5260                                                        -(2*(f*u+d)*sqrt(z)
5261                                                         +c*u+b)
5262                                                         ^2
5263                                                         /(4*(f*u+d)))
5264                                      *(c*u+b)*(2*(f*u+d)*sqrt(z)+c*u+b)
5265                                      +2*gamma_incomplete((j+i+2)/2,
5266                                                          -(2*(f*u+d)*sqrt(z)
5267                                                           +c*u+b)
5268                                                           ^2
5269                                                           /(4*(f*u+d)))
5270                                        *(f*u+d)
5271                                        *sqrt(
5272                                         (2*(f*u+d)*sqrt(z)+c*u+b)^2/(f*u+d)))
5273                            /((2*(f*u+d)*sqrt(z)+c*u+b)^2/(-f*u-d))
5274                             ^((j+i+1)/2),i,0,j),j,0,n))
5275           *(%e^(f*z+c*sqrt(z)+g))^u
5276           *%e^(-f*u*z-c*u*sqrt(z)-(c*u+b)^2/(4*(f*u+d)))
5277  /(f*u+d)^(2*(n+1))));
5278 0;
5279
5280 /* ----- Involving z^n*%e^(b*z^r+d*z+e)*(%e^(c*z^r+f*z+g))^u ---------------- */
5281
5282 /* Problem 726: NEW 9-1 */
5283 expand(niceindices(integrate(z^n*%e^(e+d*z+b*z^2)*(%e^(g+f*z+c*z^2))^u,z))-
5284 (-(c*u+b)^(-n-1)*(%e^(z*(c*z+f)+g))^u
5285                *%e^(-z*(c*u*z+b*z+f*u+d)+z*(b*z+d)-(f*u+d)^2/(4*(c*u+b))+e)
5286                *('sum(gamma_incomplete((i+1)/2,
5287                                        -(2*(c*u+b)*z+f*u+d)^2/(4*(c*u+b)))
5288                        *2^(i-n)*binomial(n,i)*(-f*u-d)^(n-i)
5289                        *(2*(c*u+b)*z+f*u+d)^(i+1)
5290                        /((2*(c*u+b)*z+f*u+d)^2/(-c*u-b))^((i+1)/2),i,0,n))
5291  /2));
5292 0;
5293
5294 /* Problem 727: NEW 10-1 */
5295 expand(niceindices(integrate(z^n*%e^(e+d*z+b*sqrt(z))*(%e^(g+f*z+c*sqrt(z)))^u,z))-
5296 (2^(-2*n-1)*('sum(4^j*binomial(n,j)
5297                     *'sum((-1)^(i-j)*binomial(j,i)*(c*u+b)^(2*n-j-i)
5298                                     *(2*(f*u+d)*sqrt(z)+c*u+b)^(j+i)
5299                                     *(gamma_incomplete((j+i+1)/2,
5300                                                        -(2*(f*u+d)*sqrt(z)
5301                                                         +c*u+b)
5302                                                         ^2
5303                                                         /(4*(f*u+d)))
5304                                      *(c*u+b)*(2*(f*u+d)*sqrt(z)+c*u+b)
5305                                      +2*gamma_incomplete((j+i+2)/2,
5306                                                          -(2*(f*u+d)*sqrt(z)
5307                                                           +c*u+b)
5308                                                           ^2
5309                                                           /(4*(f*u+d)))
5310                                        *(f*u+d)
5311                                        *sqrt(
5312                                         (2*(f*u+d)*sqrt(z)+c*u+b)^2/(f*u+d)))
5313                            /((2*(f*u+d)*sqrt(z)+c*u+b)^2/(-f*u-d))
5314                             ^((j+i+1)/2),i,0,j),j,0,n))
5315           *(%e^(f*z+c*sqrt(z)+g))^u
5316           *%e^(-f*u*z-c*u*sqrt(z)-(c*u+b)^2/(4*(f*u+d))+e)
5317  /(f*u+d)^(2*(n+1))));
5318 0;
5319
5320 /* ----- Involving z^(v-1)*(%e^(c*z))^q*(%e^(a*z))^u ------------------------ */
5321
5322 /* Problem 728: NEW 7-1 */
5323 diffcheck(integrate(z^(v-1)*(%e^(d*z))^q*(%e^(f*z))^u,z),z,factor);
5324 z^(v-1)*(%e^(d*z))^q*(%e^(f*z))^u;
5325
5326 /* Problem 729: NEW 7-1 */
5327 diffcheck(integrate(z^n*(%e^(d*z))^q*(%e^(f*z))^u,z),z,factor);
5328 z^n*(%e^(d*z))^q*(%e^(f*z))^u;
5329
5330 /* Problem 730: NEW 7-1 */
5331 diffcheck(integrate(z^(1/2+n)*(%e^(d*z))^q*(%e^(f*z))^u,z),z,factor);
5332 z^(1/2+n)*(%e^(d*z))^q*(%e^(f*z))^u;
5333
5334 /* ----- Involving z^(v-1)*(%e^(c*z))^q*(%e^(a*z+b))^u ---------------------- */
5335
5336 /* Problem 731: NEW 7-1 */
5337 diffcheck(integrate(z^(v-1)*(%e^(d*z))^q*(%e^(g+f*z))^u,z),z,factor);
5338 z^(v-1)*(%e^(d*z))^q*(%e^(g+f*z))^u;
5339
5340 /* Problem 732: NEW 7-1 */
5341 diffcheck(integrate(z^n*(%e^(d*z))^q*(%e^(g+f*z))^u,z),z,factor);
5342 z^n*(%e^(d*z))^q*(%e^(g+f*z))^u;
5343
5344 /* Problem 733: NEW 7-1 */
5345 diffcheck(integrate(z^(1/2+n)*(%e^(d*z))^q*(%e^(g+f*z))^u,z),z,factor);
5346 z^(1/2+n)*(%e^(d*z))^q*(%e^(g+f*z))^u;
5347
5348 /* ----- Involving z^(v-1)*(%e^(c*z+d))^q*(%e^(a*z+b))^u -------------------- */
5349
5350 /* Problem 734: NEW 7-1 */
5351 diffcheck(integrate(z^(v-1)*(%e^(e+d*z))^q*(%e^(g+f*z))^u,z),z,factor);
5352 z^(v-1)*(%e^(e+d*z))^q*(%e^(g+f*z))^u;
5353
5354 /* Problem 735: NEW 7-1 */
5355 diffcheck(integrate(z^n*(%e^(e+d*z))^q*(%e^(g+f*z))^u,z),z,factor);
5356 z^n*(%e^(e+d*z))^q*(%e^(g+f*z))^u;
5357
5358 /* Problem 736: NEW 7-1 */
5359 diffcheck(integrate(z^(1/2+n)*(%e^(e+d*z))^q*(%e^(g+f*z))^u,z),z,factor);
5360 z^(1/2+n)*(%e^(e+d*z))^q*(%e^(g+f*z))^u;
5361
5362 /* ----- Involving z^n*(%e^(d*z))^q*(%e^(c*z^r))^u -------------------------- */
5363
5364 /* Problem 737: NEW 9-1 */
5365 expand(niceindices(integrate(z^n*(%e^(d*z))^q*(%e^(c*z^2))^u,z))-
5366 (-c^(-n-1)*u^(-n-1)*(%e^(d*z))^q*%e^(-z*(c*u*z+d*q)-d^2*q^2/(4*c*u))
5367          *(%e^(c*z^2))^u
5368          *('sum(d^(n-i)*gamma_incomplete((i+1)/2,-(2*c*u*z+d*q)^2/(4*c*u))
5369                        *(-1)^(i-n)*2^(i-n)*binomial(n,i)*q^(n-i)
5370                        *(2*c*u*z+d*q)^(i+1)
5371                  /(-(2*c*u*z+d*q)^2/(c*u))^((i+1)/2),i,0,n))
5372  /2));
5373 0;
5374
5375 /* Problem 738: NEW 10-1 */
5376 expand(niceindices(integrate(z^n*(%e^(d*z))^q*(%e^(c*sqrt(z)))^u,z))-
5377 (2^(-2*n-1)*('sum(4^j*binomial(n,j)
5378                     *'sum(c^(2*n-j-i)*(-1)^(i-j)*binomial(j,i)*u^(2*n-j-i)
5379                                      *(2*d*q*sqrt(z)+c*u)^(j+i)
5380                                      *(c
5381                                       *gamma_incomplete((j+i+1)/2,
5382                                                         -(2*d*q*sqrt(z)+c*u)^2
5383                                                          /(4*d*q))*u
5384                                       *(2*d*q*sqrt(z)+c*u)
5385                                       +2*d
5386                                         *gamma_incomplete((j+i+2)/2,
5387                                                           -(2*d*q*sqrt(z)+c*u)
5388                                                            ^2
5389                                                            /(4*d*q))*q
5390                                         *sqrt((2*d*q*sqrt(z)+c*u)^2/(d*q)))
5391                            /(-(2*d*q*sqrt(z)+c*u)^2/(d*q))^((j+i+1)/2),i,0,j),
5392                  j,0,n))*(%e^(c*sqrt(z)))^u*(%e^(d*z))^q
5393           *%e^(-d*q*z-c*u*sqrt(z)-c^2*u^2/(4*d*q))
5394  /(d^(2*(n+1))*q^(2*(n+1)))));
5395 0;
5396
5397 /* ----- Involving z^n*(%e^(d*z+e))^q*(%e^(c*z^r))^u ------------------------ */
5398
5399 /* Problem 739: NEW 9-1 */
5400 expand(niceindices(integrate(z^n*(%e^(e+d*z))^q*(%e^(c*z^2))^u,z)) -
5401 (-c^(-n-1)*u^(-n-1)*(%e^(d*z+e))^q*%e^(-z*(c*u*z+d*q)-d^2*q^2/(4*c*u))
5402          *(%e^(c*z^2))^u
5403          *('sum(d^(n-i)*gamma_incomplete((i+1)/2,-(2*c*u*z+d*q)^2/(4*c*u))
5404                        *(-1)^(i-n)*2^(i-n)*binomial(n,i)*q^(n-i)
5405                        *(2*c*u*z+d*q)^(i+1)
5406                  /(-(2*c*u*z+d*q)^2/(c*u))^((i+1)/2),i,0,n))
5407  /2));
5408 0;
5409
5410 /* Problem 740: NEW 10-1 */
5411 expand(niceindices(integrate(z^n*(%e^(e+d*z))^q*(%e^(c*sqrt(z)))^u,z))-
5412 (2^(-2*n-1)*('sum(4^j*binomial(n,j)
5413                     *'sum(c^(2*n-j-i)*(-1)^(i-j)*binomial(j,i)*u^(2*n-j-i)
5414                                      *(2*d*q*sqrt(z)+c*u)^(j+i)
5415                                      *(c
5416                                       *gamma_incomplete((j+i+1)/2,
5417                                                         -(2*d*q*sqrt(z)+c*u)^2
5418                                                          /(4*d*q))*u
5419                                       *(2*d*q*sqrt(z)+c*u)
5420                                       +2*d
5421                                         *gamma_incomplete((j+i+2)/2,
5422                                                           -(2*d*q*sqrt(z)+c*u)
5423                                                            ^2
5424                                                            /(4*d*q))*q
5425                                         *sqrt((2*d*q*sqrt(z)+c*u)^2/(d*q)))
5426                            /(-(2*d*q*sqrt(z)+c*u)^2/(d*q))^((j+i+1)/2),i,0,j),
5427                  j,0,n))*(%e^(c*sqrt(z)))^u*(%e^(d*z+e))^q
5428           *%e^(-d*q*z-c*u*sqrt(z)-c^2*u^2/(4*d*q))
5429  /(d^(2*(n+1))*q^(2*(n+1)))));
5430 0;
5431
5432 /* ----- Involving z^(v-1)*(%e^(b*z^r))^q*(%e^(c*z^r))^u -------------------- */
5433
5434 /* Problem 741: NEW 7-1 */
5435 diffcheck(integrate(z^(v-1)*(%e^(b*z^r))^q*(%e^(c*z^r))^u,z),z,factor);
5436 z^(v-1)*(%e^(b*z^r))^q*(%e^(c*z^r))^u;
5437
5438 /* Problem 742: NEW 7-1 */
5439 diffcheck(integrate(z^n*(%e^(b*z^2))^q*(%e^(c*z^2))^u,z),z,factor);
5440 z^n*(%e^(b*z^2))^q*(%e^(c*z^2))^u;
5441
5442 /* Problem 743: NEW 7-1 */
5443 diffcheck(integrate(z^(2*n)*(%e^(b*z^2))^q*(%e^(c*z^2))^u,z),z,factor);
5444 z^(2*n)*(%e^(b*z^2))^q*(%e^(c*z^2))^u;
5445
5446 /* Problem 744: NEW 7-1 */
5447 diffcheck(integrate(z^(1+2*n)*(%e^(b*z^2))^q*(%e^(c*z^2))^u,z),z,factor);
5448 z^(1+2*n)*(%e^(b*z^2))^q*(%e^(c*z^2))^u;
5449
5450 /* Problem 745: NEW 7-1 */
5451 diffcheck(integrate(z^n*(%e^(b*sqrt(z)))^q*(%e^(c*sqrt(z)))^u,z),z,factor);
5452 z^n*(%e^(b*sqrt(z)))^q*(%e^(c*sqrt(z)))^u;
5453
5454 /* ----- Involving z^n*(%e^(d*z)^q*(%e^(c*z^r+g))^u ------------------------- */
5455
5456 /* Problem 746: NEW 9-1 */
5457 expand(niceindices(integrate(z^n*(%e^(d*z))^q*(%e^(g+c*z^2))^u,z))-
5458 (-c^(-n-1)*u^(-n-1)*(%e^(d*z))^q*%e^(-z*(c*u*z+d*q)-d^2*q^2/(4*c*u))
5459          *(%e^(c*z^2+g))^u
5460          *('sum(d^(n-i)*gamma_incomplete((i+1)/2,-(2*c*u*z+d*q)^2/(4*c*u))
5461                        *(-1)^(i-n)*2^(i-n)*binomial(n,i)*q^(n-i)
5462                        *(2*c*u*z+d*q)^(i+1)
5463                  /(-(2*c*u*z+d*q)^2/(c*u))^((i+1)/2),i,0,n))
5464  /2));
5465 0;
5466
5467 /* Problem 747: NEW 10-1 */
5468 expand(niceindices(integrate(z^n*(%e^(d*z))^q*(%e^(g+c*sqrt(z)))^u,z))-
5469 (2^(-2*n-1)*('sum(4^j*binomial(n,j)
5470                     *'sum(c^(2*n-j-i)*(-1)^(i-j)*binomial(j,i)*u^(2*n-j-i)
5471                                      *(2*d*q*sqrt(z)+c*u)^(j+i)
5472                                      *(c
5473                                       *gamma_incomplete((j+i+1)/2,
5474                                                         -(2*d*q*sqrt(z)+c*u)^2
5475                                                          /(4*d*q))*u
5476                                       *(2*d*q*sqrt(z)+c*u)
5477                                       +2*d
5478                                         *gamma_incomplete((j+i+2)/2,
5479                                                           -(2*d*q*sqrt(z)+c*u)
5480                                                            ^2
5481                                                            /(4*d*q))*q
5482                                         *sqrt((2*d*q*sqrt(z)+c*u)^2/(d*q)))
5483                            /(-(2*d*q*sqrt(z)+c*u)^2/(d*q))^((j+i+1)/2),i,0,j),
5484                  j,0,n))*(%e^(c*sqrt(z)+g))^u*(%e^(d*z))^q
5485           *%e^(-d*q*z-c*u*sqrt(z)-c^2*u^2/(4*d*q))
5486  /(d^(2*(n+1))*q^(2*(n+1)))));
5487 0;
5488
5489 /* ----- Involving z^n*(%e^(d*z+e)^q*(%e^(c*z^r+g))^u ----------------------- */
5490
5491 /* Problem 748: NEW 9-1 */
5492 expand(niceindices(integrate(z^n*(%e^(e+d*z))^q*(%e^(g+c*z^2))^u,z))-
5493 (-c^(-n-1)*u^(-n-1)*(%e^(d*z+e))^q*%e^(-z*(c*u*z+d*q)-d^2*q^2/(4*c*u))
5494          *(%e^(c*z^2+g))^u
5495          *('sum(d^(n-i)*gamma_incomplete((i+1)/2,-(2*c*u*z+d*q)^2/(4*c*u))
5496                        *(-1)^(i-n)*2^(i-n)*binomial(n,i)*q^(n-i)
5497                        *(2*c*u*z+d*q)^(i+1)
5498                  /(-(2*c*u*z+d*q)^2/(c*u))^((i+1)/2),i,0,n))
5499  /2));
5500 0;
5501
5502 /* Problem 749: NEW 10-1 */
5503 expand(niceindices(integrate(z^n*(%e^(e+d*z))^q*(%e^(g+c*sqrt(z)))^u,z))-
5504 (2^(-2*n-1)*('sum(4^j*binomial(n,j)
5505                     *'sum(c^(2*n-j-i)*(-1)^(i-j)*binomial(j,i)*u^(2*n-j-i)
5506                                      *(2*d*q*sqrt(z)+c*u)^(j+i)
5507                                      *(c
5508                                       *gamma_incomplete((j+i+1)/2,
5509                                                         -(2*d*q*sqrt(z)+c*u)^2
5510                                                          /(4*d*q))*u
5511                                       *(2*d*q*sqrt(z)+c*u)
5512                                       +2*d
5513                                         *gamma_incomplete((j+i+2)/2,
5514                                                           -(2*d*q*sqrt(z)+c*u)
5515                                                            ^2
5516                                                            /(4*d*q))*q
5517                                         *sqrt((2*d*q*sqrt(z)+c*u)^2/(d*q)))
5518                            /(-(2*d*q*sqrt(z)+c*u)^2/(d*q))^((j+i+1)/2),i,0,j),
5519                  j,0,n))*(%e^(c*sqrt(z)+g))^u*(%e^(d*z+e))^q
5520           *%e^(-d*q*z-c*u*sqrt(z)-c^2*u^2/(4*d*q))
5521  /(d^(2*(n+1))*q^(2*(n+1)))));
5522 0;
5523
5524 /* ----- Involving z^(v-1)*(%e^(b*z^r)^q*(%e^(c*z^r+g))^u ------------------- */
5525
5526 /* Problem 750: NEW 7-1 */
5527 diffcheck(integrate(z^(v-1)*(%e^(b*z^r))^q*(%e^(g+c*z^r))^u,z),z,factor);
5528 z^(v-1)*(%e^(b*z^r))^q*(%e^(g+c*z^r))^u;
5529
5530 /* Problem 751: NEW 7-1 */
5531 diffcheck(integrate(z^n*(%e^(b*z^2))^q*(%e^(g+c*z^2))^u,z),z,factor);
5532 z^n*(%e^(b*z^2))^q*(%e^(g+c*z^2))^u;
5533
5534 /* Problem 752: NEW 7-1 */
5535 diffcheck(integrate(z^(2*n)*(%e^(b*z^2))^q*(%e^(g+c*z^2))^u,z),z,factor);
5536 z^(2*n)*(%e^(b*z^2))^q*(%e^(g+c*z^2))^u;
5537
5538 /* Problem 753: NEW 7-1 */
5539 diffcheck(integrate(z^(1+2*n)*(%e^(b*z^2))^q*(%e^(g+c*z^2))^u,z),z,factor);
5540 z^(1+2*n)*(%e^(b*z^2))^q*(%e^(g+c*z^2))^u;
5541
5542 /* Problem 754: NEW 7-1 */
5543 diffcheck(integrate(z^n*(%e^(b*sqrt(z)))^q*(%e^(g+c*sqrt(z)))^u,z),z,factor);
5544 z^n*(%e^(b*sqrt(z)))^q*(%e^(g+c*sqrt(z)))^u;
5545
5546 /* ----- Involving z^(v-1)*(%e^(b*z^r+e)^q*(%e^(c*z^r+g))^u ----------------- */
5547
5548 /* Problem 755: NEW 7-1 */
5549 diffcheck(integrate(z^(v-1)*(%e^(e+b*z^r))^q*(%e^(g+c*z^r))^u,z),z,factor);
5550 z^(v-1)*(%e^(e+b*z^r))^q*(%e^(g+c*z^r))^u;
5551
5552 /* Problem 756: NEW 7-1 */
5553 diffcheck(integrate(z^n*(%e^(e+b*z^2))^q*(%e^(g+c*z^2))^u,z),z,factor);
5554 z^n*(%e^(e+b*z^2))^q*(%e^(g+c*z^2))^u;
5555
5556 /* Problem 757: NEW 7-1 */
5557 diffcheck(integrate(z^(2*n)*(%e^(e+b*z^2))^q*(%e^(g+c*z^2))^u,z),z,factor);
5558 z^(2*n)*(%e^(e+b*z^2))^q*(%e^(g+c*z^2))^u;
5559
5560 /* Problem 758: NEW 7-1 */
5561 diffcheck(integrate(z^(1+2*n)*(%e^(e+b*z^2))^q*(%e^(g+c*z^2))^u,z),z,factor);
5562 z^(1+2*n)*(%e^(e+b*z^2))^q*(%e^(g+c*z^2))^u;
5563
5564 /* Problem 759: NEW 7-1 */
5565 diffcheck(integrate(z^n*(%e^(e+b*sqrt(z)))^q*(%e^(g+c*sqrt(z)))^u,z),z,factor);
5566 z^n*(%e^(e+b*sqrt(z)))^q*(%e^(g+c*sqrt(z)))^u;
5567
5568 /* ----- Involving z^n*(%e^(d*z)^q*(%e^(c*z^r+f*z))^u ----------------------- */
5569
5570 /* Problem 760: NEW 9-1 */
5571 expand(niceindices(integrate(z^n*(%e^(d*z))^q*(%e^(f*z+c*z^2))^u,z))-
5572 (-c^(-n-1)*u^(-n-1)*(%e^(d*z))^q*(%e^(z*(c*z+f)))^u
5573          *%e^(-z*(c*u*z+f*u+d*q)-(f*u+d*q)^2/(4*c*u))
5574          *('sum(gamma_incomplete((i+1)/2,-(2*c*u*z+f*u+d*q)^2/(4*c*u))
5575                  *2^(i-n)*binomial(n,i)*(-f*u-d*q)^(n-i)
5576                  *(2*c*u*z+f*u+d*q)^(i+1)
5577                  /(-(2*c*u*z+f*u+d*q)^2/(c*u))^((i+1)/2),i,0,n))
5578  /2));
5579 0;
5580
5581 /* Problem 761: NEW 10-1 */
5582 expand(niceindices(integrate(z^n*(%e^(d*z))^q*(%e^(f*z+c*sqrt(z)))^u,z))-
5583 (2^(-2*n-1)*('sum(4^j*binomial(n,j)
5584                     *'sum(c^(2*n-j-i)*(-1)^(i-j)*binomial(j,i)*u^(2*n-j-i)
5585                                      *(2*(f*u+d*q)*sqrt(z)+c*u)^(j+i)
5586                                      *(c
5587                                       *gamma_incomplete((j+i+1)/2,
5588                                                         -(2*(f*u+d*q)*sqrt(z)
5589                                                          +c*u)
5590                                                          ^2
5591                                                          /(4*(f*u+d*q)))*u
5592                                       *(2*(f*u+d*q)*sqrt(z)+c*u)
5593                                       +2
5594                                        *gamma_incomplete((j+i+2)/2,
5595                                                          -(2*(f*u+d*q)*sqrt(z)
5596                                                           +c*u)
5597                                                           ^2
5598                                                           /(4*(f*u+d*q)))
5599                                        *(f*u+d*q)
5600                                        *sqrt(
5601                                         (2*(f*u+d*q)*sqrt(z)+c*u)^2
5602                                          /(f*u+d*q)))
5603                            /((2*(f*u+d*q)*sqrt(z)+c*u)^2/(-f*u-d*q))
5604                             ^((j+i+1)/2),i,0,j),j,0,n))*(%e^(d*z))^q
5605           *(%e^(f*z+c*sqrt(z)))^u
5606           *%e^(-f*u*z-d*q*z-c*u*sqrt(z)-c^2*u^2/(4*(f*u+d*q)))
5607  /(f*u+d*q)^(2*(n+1))));
5608 0;
5609
5610 /* ----- Involving z^n*(%e^(d*z+e)^q*(%e^(c*z^r+f*z))^u --------------------- */
5611
5612 /* Problem 762: NEW 9-1 */
5613 expand(niceindices(integrate(z^n*(%e^(e+d*z))^q*(%e^(f*z+c*z^2))^u,z))-
5614 (-c^(-n-1)*u^(-n-1)*(%e^(z*(c*z+f)))^u*(%e^(d*z+e))^q
5615          *%e^(-z*(c*u*z+f*u+d*q)-(f*u+d*q)^2/(4*c*u))
5616          *('sum(gamma_incomplete((i+1)/2,-(2*c*u*z+f*u+d*q)^2/(4*c*u))
5617                  *2^(i-n)*binomial(n,i)*(-f*u-d*q)^(n-i)
5618                  *(2*c*u*z+f*u+d*q)^(i+1)
5619                  /(-(2*c*u*z+f*u+d*q)^2/(c*u))^((i+1)/2),i,0,n))
5620  /2));
5621 0;
5622
5623 /* Problem 763: NEW 10-1 */
5624 expand(niceindices(integrate(z^n*(%e^(e+d*z))^q*(%e^(f*z+c*sqrt(z)))^u,z))-
5625 (2^(-2*n-1)*('sum(4^j*binomial(n,j)
5626                     *'sum(c^(2*n-j-i)*(-1)^(i-j)*binomial(j,i)*u^(2*n-j-i)
5627                                      *(2*(f*u+d*q)*sqrt(z)+c*u)^(j+i)
5628                                      *(c
5629                                       *gamma_incomplete((j+i+1)/2,
5630                                                         -(2*(f*u+d*q)*sqrt(z)
5631                                                          +c*u)
5632                                                          ^2
5633                                                          /(4*(f*u+d*q)))*u
5634                                       *(2*(f*u+d*q)*sqrt(z)+c*u)
5635                                       +2
5636                                        *gamma_incomplete((j+i+2)/2,
5637                                                          -(2*(f*u+d*q)*sqrt(z)
5638                                                           +c*u)
5639                                                           ^2
5640                                                           /(4*(f*u+d*q)))
5641                                        *(f*u+d*q)
5642                                        *sqrt(
5643                                         (2*(f*u+d*q)*sqrt(z)+c*u)^2
5644                                          /(f*u+d*q)))
5645                            /((2*(f*u+d*q)*sqrt(z)+c*u)^2/(-f*u-d*q))
5646                             ^((j+i+1)/2),i,0,j),j,0,n))*(%e^(d*z+e))^q
5647           *(%e^(f*z+c*sqrt(z)))^u
5648           *%e^(-f*u*z-d*q*z-c*u*sqrt(z)-c^2*u^2/(4*(f*u+d*q)))
5649  /(f*u+d*q)^(2*(n+1))));
5650 0;
5651
5652 /* ----- Involving z^n*(%e^(b*z^r)^q*(%e^(c*z^r+f*z))^u --------------------- */
5653
5654 /* Problem 764: NEW 9-1 */
5655 expand(niceindices(integrate(z^n*(%e^(b*z^2))^q*(%e^(f*z+c*z^2))^u,z))-
5656 (-(c*u+b*q)^(-n-1)*(%e^(z*(c*z+f)))^u
5657                  *%e^(-z*(c*u*z+b*q*z+f*u)-f^2*u^2/(4*(c*u+b*q)))
5658                  *(%e^(b*z^2))^q
5659                  *('sum(f^(n-i)*gamma_incomplete((i+1)/2,
5660                                                  -(2*(c*u+b*q)*z+f*u)^2
5661                                                   /(4*(c*u+b*q)))*(-1)^(i-n)
5662                                *2^(i-n)*binomial(n,i)*u^(n-i)
5663                                *(2*(c*u+b*q)*z+f*u)^(i+1)
5664                          /((2*(c*u+b*q)*z+f*u)^2/(-c*u-b*q))^((i+1)/2),i,0,n))
5665  /2));
5666 0;
5667
5668 /* Problem 765: NEW 10-1 */
5669 expand(niceindices(integrate(z^n*(%e^(b*sqrt(z)))^q*(%e^(f*z+c*sqrt(z)))^u,z))-
5670 (2^(-2*n-1)*('sum(4^j*binomial(n,j)
5671                     *'sum((-1)^(i-j)*binomial(j,i)*(c*u+b*q)^(2*n-j-i)
5672                                     *(2*f*u*sqrt(z)+c*u+b*q)^(j+i)
5673                                     *(gamma_incomplete((j+i+1)/2,
5674                                                        -(2*f*u*sqrt(z)
5675                                                         +c*u+b*q)
5676                                                         ^2
5677                                                         /(4*f*u))
5678                                      *(c*u+b*q)*(2*f*u*sqrt(z)+c*u+b*q)
5679                                      +2*f
5680                                        *gamma_incomplete((j+i+2)/2,
5681                                                          -(2*f*u*sqrt(z)
5682                                                           +c*u+b*q)
5683                                                           ^2
5684                                                           /(4*f*u))*u
5685                                        *sqrt((2*f*u*sqrt(z)+c*u+b*q)^2/(f*u)))
5686                            /(-(2*f*u*sqrt(z)+c*u+b*q)^2/(f*u))^((j+i+1)/2),i,
5687                           0,j),j,0,n))*(%e^(b*sqrt(z)))^q
5688           *(%e^(f*z+c*sqrt(z)))^u
5689           *%e^(-f*u*z-c*u*sqrt(z)-b*q*sqrt(z)-(c*u+b*q)^2/(4*f*u))
5690  /(f^(2*(n+1))*u^(2*(n+1)))));
5691 0;
5692
5693 /* ----- Involving z^n*(%e^(b*z^r+e)^q*(%e^(c*z^r+f*z))^u ------------------- */
5694
5695 /* Problem 766: NEW 9-1 */
5696 expand(niceindices(integrate(z^n*(%e^(e+b*z^2))^q*(%e^(f*z+c*z^2))^u,z))-
5697 (-(c*u+b*q)^(-n-1)*(%e^(z*(c*z+f)))^u
5698                  *%e^(-z*(c*u*z+b*q*z+f*u)-f^2*u^2/(4*(c*u+b*q)))
5699                  *(%e^(b*z^2+e))^q
5700                  *('sum(f^(n-i)*gamma_incomplete((i+1)/2,
5701                                                  -(2*(c*u+b*q)*z+f*u)^2
5702                                                   /(4*(c*u+b*q)))*(-1)^(i-n)
5703                                *2^(i-n)*binomial(n,i)*u^(n-i)
5704                                *(2*(c*u+b*q)*z+f*u)^(i+1)
5705                          /((2*(c*u+b*q)*z+f*u)^2/(-c*u-b*q))^((i+1)/2),i,0,n))
5706  /2));
5707 0;
5708
5709 /* Problem 767: NEW 10-1 */
5710 expand(niceindices(integrate(z^n*(%e^(e+b*sqrt(z)))^q*(%e^(f*z+c*sqrt(z)))^u,z))-
5711 (2^(-2*n-1)*('sum(4^j*binomial(n,j)
5712                     *'sum((-1)^(i-j)*binomial(j,i)*(c*u+b*q)^(2*n-j-i)
5713                                     *(2*f*u*sqrt(z)+c*u+b*q)^(j+i)
5714                                     *(gamma_incomplete((j+i+1)/2,
5715                                                        -(2*f*u*sqrt(z)
5716                                                         +c*u+b*q)
5717                                                         ^2
5718                                                         /(4*f*u))
5719                                      *(c*u+b*q)*(2*f*u*sqrt(z)+c*u+b*q)
5720                                      +2*f
5721                                        *gamma_incomplete((j+i+2)/2,
5722                                                          -(2*f*u*sqrt(z)
5723                                                           +c*u+b*q)
5724                                                           ^2
5725                                                           /(4*f*u))*u
5726                                        *sqrt((2*f*u*sqrt(z)+c*u+b*q)^2/(f*u)))
5727                            /(-(2*f*u*sqrt(z)+c*u+b*q)^2/(f*u))^((j+i+1)/2),i,
5728                           0,j),j,0,n))*(%e^(b*sqrt(z)+e))^q
5729           *(%e^(f*z+c*sqrt(z)))^u
5730           *%e^(-f*u*z-c*u*sqrt(z)-b*q*sqrt(z)-(c*u+b*q)^2/(4*f*u))
5731  /(f^(2*(n+1))*u^(2*(n+1)))));
5732 0;
5733
5734 /* ----- Involving z^n*(%e^(b*z^r+d*z)^q*(%e^(c*z^r+f*z))^u ----------------- */
5735
5736 /* Problem 768: NEW 9-1 */
5737 expand(niceindices(integrate(z^n*(%e^(d*z+b*z^2))^q*(%e^(f*z+c*z^2))^u,z))-
5738 (-(c*u+b*q)^(-n-1)*(%e^(z*(b*z+d)))^q*(%e^(z*(c*z+f)))^u
5739                  *%e^(-z*(c*u*z+b*q*z+f*u+d*q)-(f*u+d*q)^2/(4*(c*u+b*q)))
5740                  *('sum(gamma_incomplete((i+1)/2,
5741                                          -(2*(c*u+b*q)*z+f*u+d*q)^2
5742                                           /(4*(c*u+b*q)))
5743                          *2^(i-n)*binomial(n,i)*(-f*u-d*q)^(n-i)
5744                          *(2*(c*u+b*q)*z+f*u+d*q)^(i+1)
5745                          /((2*(c*u+b*q)*z+f*u+d*q)^2/(-c*u-b*q))^((i+1)/2),i,
5746                         0,n))
5747  /2));
5748 0;
5749
5750 /* Problem 769: NEW 10-1 */
5751 expand(niceindices(integrate(z^n*(%e^(d*z+b*sqrt(z)))^q*(%e^(f*z+c*sqrt(z)))^u,z))-
5752 (2^(-2*n-1)*('sum(4^j*binomial(n,j)
5753                     *'sum((-1)^(i-j)*binomial(j,i)*(c*u+b*q)^(2*n-j-i)
5754                                     *(2*(f*u+d*q)*sqrt(z)+c*u+b*q)^(j+i)
5755                                     *(gamma_incomplete((j+i+1)/2,
5756                                                        -(2*(f*u+d*q)*sqrt(z)
5757                                                         +c*u+b*q)
5758                                                         ^2
5759                                                         /(4*(f*u+d*q)))
5760                                      *(c*u+b*q)*(2*(f*u+d*q)*sqrt(z)+c*u+b*q)
5761                                      +2*gamma_incomplete((j+i+2)/2,
5762                                                          -(2*(f*u+d*q)*sqrt(z)
5763                                                           +c*u+b*q)
5764                                                           ^2
5765                                                           /(4*(f*u+d*q)))
5766                                        *(f*u+d*q)
5767                                        *sqrt(
5768                                         (2*(f*u+d*q)*sqrt(z)+c*u+b*q)^2
5769                                          /(f*u+d*q)))
5770                            /((2*(f*u+d*q)*sqrt(z)+c*u+b*q)^2/(-f*u-d*q))
5771                             ^((j+i+1)/2),i,0,j),j,0,n))*(%e^(d*z+b*sqrt(z)))^q
5772           *(%e^(f*z+c*sqrt(z)))^u
5773           *%e^(-f*u*z-d*q*z-c*u*sqrt(z)-b*q*sqrt(z)-(c*u+b*q)^2/(4*(f*u+d*q)))
5774  /(f*u+d*q)^(2*(n+1))));
5775 0;
5776
5777 /* ----- Involving z^n*(%e^(d*z)^q*(%e^(c*z^r+f*z+g))^u --------------------- */
5778
5779 /* Problem 770: NEW 9-1 */
5780 expand(niceindices(integrate(z^n*(%e^(d*z))^q*(%e^(g+f*z+c*z^2))^u,z))-
5781 (-c^(-n-1)*u^(-n-1)*(%e^(d*z))^q*(%e^(z*(c*z+f)+g))^u
5782          *%e^(-z*(c*u*z+f*u+d*q)-(f*u+d*q)^2/(4*c*u))
5783          *('sum(gamma_incomplete((i+1)/2,-(2*c*u*z+f*u+d*q)^2/(4*c*u))
5784                  *2^(i-n)*binomial(n,i)*(-f*u-d*q)^(n-i)
5785                  *(2*c*u*z+f*u+d*q)^(i+1)
5786                  /(-(2*c*u*z+f*u+d*q)^2/(c*u))^((i+1)/2),i,0,n))
5787  /2));
5788 0;
5789
5790 /* Problem 771: NEW 10-1 */
5791 expand(niceindices(integrate(z^n*(%e^(d*z))^q*(%e^(g+f*z+c*sqrt(z)))^u,z))-
5792 (2^(-2*n-1)*('sum(4^j*binomial(n,j)
5793                     *'sum(c^(2*n-j-i)*(-1)^(i-j)*binomial(j,i)*u^(2*n-j-i)
5794                                      *(2*(f*u+d*q)*sqrt(z)+c*u)^(j+i)
5795                                      *(c
5796                                       *gamma_incomplete((j+i+1)/2,
5797                                                         -(2*(f*u+d*q)*sqrt(z)
5798                                                          +c*u)
5799                                                          ^2
5800                                                          /(4*(f*u+d*q)))*u
5801                                       *(2*(f*u+d*q)*sqrt(z)+c*u)
5802                                       +2
5803                                        *gamma_incomplete((j+i+2)/2,
5804                                                          -(2*(f*u+d*q)*sqrt(z)
5805                                                           +c*u)
5806                                                           ^2
5807                                                           /(4*(f*u+d*q)))
5808                                        *(f*u+d*q)
5809                                        *sqrt(
5810                                         (2*(f*u+d*q)*sqrt(z)+c*u)^2
5811                                          /(f*u+d*q)))
5812                            /((2*(f*u+d*q)*sqrt(z)+c*u)^2/(-f*u-d*q))
5813                             ^((j+i+1)/2),i,0,j),j,0,n))*(%e^(d*z))^q
5814           *(%e^(f*z+c*sqrt(z)+g))^u
5815           *%e^(-f*u*z-d*q*z-c*u*sqrt(z)-c^2*u^2/(4*(f*u+d*q)))
5816  /(f*u+d*q)^(2*(n+1))));
5817  0;
5818
5819 /* ----- Involving z^n*(%e^(d*z+e)^q*(%e^(c*z^r+f*z+g))^u ------------------- */
5820
5821 /* Problem 772: NEW 9-1 */
5822 expand(niceindices(integrate(z^n*(%e^(e+d*z))^q*(%e^(g+f*z+c*z^2))^u,z))-
5823 (-c^(-n-1)*u^(-n-1)*(%e^(d*z+e))^q*(%e^(z*(c*z+f)+g))^u
5824          *%e^(-z*(c*u*z+f*u+d*q)-(f*u+d*q)^2/(4*c*u))
5825          *('sum(gamma_incomplete((i+1)/2,-(2*c*u*z+f*u+d*q)^2/(4*c*u))
5826                  *2^(i-n)*binomial(n,i)*(-f*u-d*q)^(n-i)
5827                  *(2*c*u*z+f*u+d*q)^(i+1)
5828                  /(-(2*c*u*z+f*u+d*q)^2/(c*u))^((i+1)/2),i,0,n))
5829  /2));
5830 0;
5831
5832 /* Problem 773: NEW 10-1 */
5833 expand(niceindices(integrate(z^n*(%e^(e+d*z))^q*(%e^(g+f*z+c*sqrt(z)))^u,z))-
5834 (2^(-2*n-1)*('sum(4^j*binomial(n,j)
5835                     *'sum(c^(2*n-j-i)*(-1)^(i-j)*binomial(j,i)*u^(2*n-j-i)
5836                                      *(2*(f*u+d*q)*sqrt(z)+c*u)^(j+i)
5837                                      *(c
5838                                       *gamma_incomplete((j+i+1)/2,
5839                                                         -(2*(f*u+d*q)*sqrt(z)
5840                                                          +c*u)
5841                                                          ^2
5842                                                          /(4*(f*u+d*q)))*u
5843                                       *(2*(f*u+d*q)*sqrt(z)+c*u)
5844                                       +2
5845                                        *gamma_incomplete((j+i+2)/2,
5846                                                          -(2*(f*u+d*q)*sqrt(z)
5847                                                           +c*u)
5848                                                           ^2
5849                                                           /(4*(f*u+d*q)))
5850                                        *(f*u+d*q)
5851                                        *sqrt(
5852                                         (2*(f*u+d*q)*sqrt(z)+c*u)^2
5853                                          /(f*u+d*q)))
5854                            /((2*(f*u+d*q)*sqrt(z)+c*u)^2/(-f*u-d*q))
5855                             ^((j+i+1)/2),i,0,j),j,0,n))*(%e^(d*z+e))^q
5856           *(%e^(f*z+c*sqrt(z)+g))^u
5857           *%e^(-f*u*z-d*q*z-c*u*sqrt(z)-c^2*u^2/(4*(f*u+d*q)))
5858  /(f*u+d*q)^(2*(n+1))));
5859 0;
5860
5861 /* ----- Involving z^n*(%e^(b*z^r)^q*(%e^(c*z^r+f*z+g))^u ------------------- */
5862
5863 /* Problem 774: NEW 9-1 */
5864 expand(niceindices(integrate(z^n*(%e^(b*z^2))^q*(%e^(g+f*z+c*z^2))^u,z))-
5865 (-(c*u+b*q)^(-n-1)*(%e^(z*(c*z+f)+g))^u
5866                  *%e^(-z*(c*u*z+b*q*z+f*u)-f^2*u^2/(4*(c*u+b*q)))
5867                  *(%e^(b*z^2))^q
5868                  *('sum(f^(n-i)*gamma_incomplete((i+1)/2,
5869                                                  -(2*(c*u+b*q)*z+f*u)^2
5870                                                   /(4*(c*u+b*q)))*(-1)^(i-n)
5871                                *2^(i-n)*binomial(n,i)*u^(n-i)
5872                                *(2*(c*u+b*q)*z+f*u)^(i+1)
5873                          /((2*(c*u+b*q)*z+f*u)^2/(-c*u-b*q))^((i+1)/2),i,0,n))
5874  /2));
5875 0;
5876
5877 /* Problem 775: NEW 10-1 */
5878 expand(niceindices(integrate(z^n*(%e^(b*sqrt(z)))^q*(%e^(g+f*z+c*sqrt(z)))^u,z))-
5879 (2^(-2*n-1)*('sum(4^j*binomial(n,j)
5880                     *'sum((-1)^(i-j)*binomial(j,i)*(c*u+b*q)^(2*n-j-i)
5881                                     *(2*f*u*sqrt(z)+c*u+b*q)^(j+i)
5882                                     *(gamma_incomplete((j+i+1)/2,
5883                                                        -(2*f*u*sqrt(z)
5884                                                         +c*u+b*q)
5885                                                         ^2
5886                                                         /(4*f*u))
5887                                      *(c*u+b*q)*(2*f*u*sqrt(z)+c*u+b*q)
5888                                      +2*f
5889                                        *gamma_incomplete((j+i+2)/2,
5890                                                          -(2*f*u*sqrt(z)
5891                                                           +c*u+b*q)
5892                                                           ^2
5893                                                           /(4*f*u))*u
5894                                        *sqrt((2*f*u*sqrt(z)+c*u+b*q)^2/(f*u)))
5895                            /(-(2*f*u*sqrt(z)+c*u+b*q)^2/(f*u))^((j+i+1)/2),i,
5896                           0,j),j,0,n))*(%e^(b*sqrt(z)))^q
5897           *(%e^(f*z+c*sqrt(z)+g))^u
5898           *%e^(-f*u*z-c*u*sqrt(z)-b*q*sqrt(z)-(c*u+b*q)^2/(4*f*u))
5899  /(f^(2*(n+1))*u^(2*(n+1)))));
5900 0;
5901
5902 /* ----- Involving z^n*(%e^(b*z^r+e)^q*(%e^(c*z^r+f*z+g))^u ----------------- */
5903
5904 /* Problem 776: NEW 9-1 */
5905 expand(niceindices(integrate(z^n*(%e^(e+b*z^2))^q*(%e^(g+f*z+c*z^2))^u,z))-
5906 (-(c*u+b*q)^(-n-1)*(%e^(z*(c*z+f)+g))^u
5907                  *%e^(-z*(c*u*z+b*q*z+f*u)-f^2*u^2/(4*(c*u+b*q)))
5908                  *(%e^(b*z^2+e))^q
5909                  *('sum(f^(n-i)*gamma_incomplete((i+1)/2,
5910                                                  -(2*(c*u+b*q)*z+f*u)^2
5911                                                   /(4*(c*u+b*q)))*(-1)^(i-n)
5912                                *2^(i-n)*binomial(n,i)*u^(n-i)
5913                                *(2*(c*u+b*q)*z+f*u)^(i+1)
5914                          /((2*(c*u+b*q)*z+f*u)^2/(-c*u-b*q))^((i+1)/2),i,0,n))
5915  /2));
5916 0;
5917
5918 /* Problem 777: NEW 10-1 */
5919 expand(niceindices(integrate(z^n*(%e^(e+b*sqrt(z)))^q*(%e^(g+f*z+c*sqrt(z)))^u,z))-
5920 (2^(-2*n-1)*('sum(4^j*binomial(n,j)
5921                     *'sum((-1)^(i-j)*binomial(j,i)*(c*u+b*q)^(2*n-j-i)
5922                                     *(2*f*u*sqrt(z)+c*u+b*q)^(j+i)
5923                                     *(gamma_incomplete((j+i+1)/2,
5924                                                        -(2*f*u*sqrt(z)
5925                                                         +c*u+b*q)
5926                                                         ^2
5927                                                         /(4*f*u))
5928                                      *(c*u+b*q)*(2*f*u*sqrt(z)+c*u+b*q)
5929                                      +2*f
5930                                        *gamma_incomplete((j+i+2)/2,
5931                                                          -(2*f*u*sqrt(z)
5932                                                           +c*u+b*q)
5933                                                           ^2
5934                                                           /(4*f*u))*u
5935                                        *sqrt((2*f*u*sqrt(z)+c*u+b*q)^2/(f*u)))
5936                            /(-(2*f*u*sqrt(z)+c*u+b*q)^2/(f*u))^((j+i+1)/2),i,
5937                           0,j),j,0,n))*(%e^(b*sqrt(z)+e))^q
5938           *(%e^(f*z+c*sqrt(z)+g))^u
5939           *%e^(-f*u*z-c*u*sqrt(z)-b*q*sqrt(z)-(c*u+b*q)^2/(4*f*u))
5940  /(f^(2*(n+1))*u^(2*(n+1)))));
5941 0;
5942
5943 /* ----- Involving z^n*(%e^(b*z^r+d*z)^q*(%e^(c*z^r+f*z+g))^u --------------- */
5944
5945 /* Problem 778: NEW 9-1 */
5946 expand(niceindices(integrate(z^n*(%e^(d*z+b*z^2))^q*(%e^(g+f*z+c*z^2))^u,z))-
5947 (-(c*u+b*q)^(-n-1)*(%e^(z*(b*z+d)))^q*(%e^(z*(c*z+f)+g))^u
5948                  *%e^(-z*(c*u*z+b*q*z+f*u+d*q)-(f*u+d*q)^2/(4*(c*u+b*q)))
5949                  *('sum(gamma_incomplete((i+1)/2,
5950                                          -(2*(c*u+b*q)*z+f*u+d*q)^2
5951                                           /(4*(c*u+b*q)))
5952                          *2^(i-n)*binomial(n,i)*(-f*u-d*q)^(n-i)
5953                          *(2*(c*u+b*q)*z+f*u+d*q)^(i+1)
5954                          /((2*(c*u+b*q)*z+f*u+d*q)^2/(-c*u-b*q))^((i+1)/2),i,
5955                         0,n))
5956  /2));
5957 0;
5958
5959 /* Problem 779: NEW 10-1 */
5960 expand(
5961   niceindices(integrate(z^n*(%e^(d*z+b*sqrt(z)))^q*(%e^(g+f*z+c*sqrt(z)))^u,z))-
5962 (2^(-2*n-1)*('sum(4^j*binomial(n,j)
5963                     *'sum((-1)^(i-j)*binomial(j,i)*(c*u+b*q)^(2*n-j-i)
5964                                     *(2*(f*u+d*q)*sqrt(z)+c*u+b*q)^(j+i)
5965                                     *(gamma_incomplete((j+i+1)/2,
5966                                                        -(2*(f*u+d*q)*sqrt(z)
5967                                                         +c*u+b*q)
5968                                                         ^2
5969                                                         /(4*(f*u+d*q)))
5970                                      *(c*u+b*q)*(2*(f*u+d*q)*sqrt(z)+c*u+b*q)
5971                                      +2*gamma_incomplete((j+i+2)/2,
5972                                                          -(2*(f*u+d*q)*sqrt(z)
5973                                                           +c*u+b*q)
5974                                                           ^2
5975                                                           /(4*(f*u+d*q)))
5976                                        *(f*u+d*q)
5977                                        *sqrt(
5978                                         (2*(f*u+d*q)*sqrt(z)+c*u+b*q)^2
5979                                          /(f*u+d*q)))
5980                            /((2*(f*u+d*q)*sqrt(z)+c*u+b*q)^2/(-f*u-d*q))
5981                             ^((j+i+1)/2),i,0,j),j,0,n))*(%e^(d*z+b*sqrt(z)))^q
5982           *(%e^(f*z+c*sqrt(z)+g))^u
5983           *%e^(-f*u*z-d*q*z-c*u*sqrt(z)-b*q*sqrt(z)-(c*u+b*q)^2/(4*(f*u+d*q)))
5984  /(f*u+d*q)^(2*(n+1))))$
5985 0;
5986
5987 /* ----- Involving z^n*(%e^(b*z^r+d*z+e)^q*(%e^(c*z^r+f*z+g))^u ------------- */
5988
5989 /* Problem 780: NEW 9-1 */
5990 expand(niceindices(integrate(z^n*(%e^(e+d*z+b*z^2))^q*(%e^(g+f*z+c*z^2))^u,z))-
5991 (-(c*u+b*q)^(-n-1)*(%e^(z*(b*z+d)+e))^q*(%e^(z*(c*z+f)+g))^u
5992                  *%e^(-z*(c*u*z+b*q*z+f*u+d*q)-(f*u+d*q)^2/(4*(c*u+b*q)))
5993                  *('sum(gamma_incomplete((i+1)/2,
5994                                          -(2*(c*u+b*q)*z+f*u+d*q)^2
5995                                           /(4*(c*u+b*q)))
5996                          *2^(i-n)*binomial(n,i)*(-f*u-d*q)^(n-i)
5997                          *(2*(c*u+b*q)*z+f*u+d*q)^(i+1)
5998                          /((2*(c*u+b*q)*z+f*u+d*q)^2/(-c*u-b*q))^((i+1)/2),i,
5999                         0,n))
6000  /2));
6001 0;
6002
6003 /* Problem 781: NEW 10-1
6004  * This result must be checked more carefully.
6005  */
6006 expand(
6007   niceindices(integrate(z^n*(%e^(e+d*z+b*sqrt(z)))^q*(%e^(g+f*z+c*sqrt(z)))^u,z))-
6008 (2^(-2*n-1)*('sum(4^j*binomial(n,j)
6009                     *'sum((-1)^(i-j)*binomial(j,i)*(c*u+b*q)^(2*n-j-i)
6010                                     *(2*(f*u+d*q)*sqrt(z)+c*u+b*q)^(j+i)
6011                                     *(gamma_incomplete((j+i+1)/2,
6012                                                        -(2*(f*u+d*q)*sqrt(z)
6013                                                         +c*u+b*q)
6014                                                         ^2
6015                                                         /(4*(f*u+d*q)))
6016                                      *(c*u+b*q)*(2*(f*u+d*q)*sqrt(z)+c*u+b*q)
6017                                      +2*gamma_incomplete((j+i+2)/2,
6018                                                          -(2*(f*u+d*q)*sqrt(z)
6019                                                           +c*u+b*q)
6020                                                           ^2
6021                                                           /(4*(f*u+d*q)))
6022                                        *(f*u+d*q)
6023                                        *sqrt(
6024                                         (2*(f*u+d*q)*sqrt(z)+c*u+b*q)^2
6025                                          /(f*u+d*q)))
6026                            /((2*(f*u+d*q)*sqrt(z)+c*u+b*q)^2/(-f*u-d*q))
6027                             ^((j+i+1)/2),i,0,j),j,0,n))
6028           *(%e^(d*z+b*sqrt(z)+e))^q*(%e^(f*z+c*sqrt(z)+g))^u
6029           *%e^(-f*u*z-d*q*z-c*u*sqrt(z)-b*q*sqrt(z)-(c*u+b*q)^2/(4*(f*u+d*q)))
6030  /(f*u+d*q)^(2*(n+1))))$
6031 0;
6032
6033 /* Involving rational functions of the direct functions and a power function  */
6034
6035 /* ----- Involving z^n/(a+b*%e^(c*z)) --------------------------------------- */
6036
6037 /* Problem 782: OK */
6038 integrate(z/(b*%e^(c*z)+a),z);
6039 log(%e^(c*z))^2/(2*a*c^2)-(log(%e^(c*z))*log(b*%e^(c*z)/a+1)
6040                           +li[2](-b*%e^(c*z)/a))
6041                           /(a*c^2)$
6042
6043 /* Problem 783: OK */
6044 integrate(z^2/(b*%e^(c*z)+a),z);
6045 2*(-log(%e^(c*z))^2*log(b*%e^(c*z)/a+1)/2
6046   +li[3](-b*%e^(c*z)/a)-log(%e^(c*z))*li[2](-b*%e^(c*z)/a))
6047  /(a*c^3)
6048  +log(%e^(c*z))^3/(3*a*c^3)$
6049
6050 /* Problem 784: OK */
6051 integrate(z^3/(b*%e^(c*z)+a),z);
6052 log(%e^(c*z))^4/(4*a*c^4)-6*(log(%e^(c*z))^3*log(b*%e^(c*z)/a+1)/6
6053                             +li[4](-b*%e^(c*z)/a)
6054                             -log(%e^(c*z))*li[3](-b*%e^(c*z)/a)
6055                             +log(%e^(c*z))^2*li[2](-b*%e^(c*z)/a)/2)
6056                           /(a*c^4)$
6057
6058 /* Problem 785: OK */
6059 integrate(z^4/(b*%e^(c*z)+a),z);
6060 24*(-log(%e^(c*z))^4*log(b*%e^(c*z)/a+1)/24
6061    +li[5](-b*%e^(c*z)/a)-log(%e^(c*z))*li[4](-b*%e^(c*z)/a)
6062    +log(%e^(c*z))^2*li[3](-b*%e^(c*z)/a)/2
6063    -log(%e^(c*z))^3*li[2](-b*%e^(c*z)/a)/6)
6064  /(a*c^5)
6065  +log(%e^(c*z))^5/(5*a*c^5)$
6066
6067 /* Problem 786: NOUN */
6068 integrate(z^n/(1-%e^(c*z)),z);
6069 'integrate(z^n/(1-%e^(c*z)),z);
6070
6071 /* ----- Involving z^n*(a+b*c^(d*z))^-m ------------------------------------- */
6072
6073 /* Problem 787: OK */
6074 expand(integrate(z/(b*c^(d*z)+a)^2,z));
6075 -log(%e^(log(c)*d*z))*log(b*%e^(log(c)*d*z)/a+1)/(a^2*log(c)^2*d^2)
6076  +log(b*%e^(log(c)*d*z)+a)/(a^2*log(c)^2*d^2)
6077  -li[2](-b*%e^(log(c)*d*z)/a)/(a^2*log(c)^2*d^2)
6078  +log(%e^(log(c)*d*z))^2/(2*a^2*log(c)^2*d^2)
6079  -log(%e^(log(c)*d*z))/(a^2*log(c)^2*d^2)
6080  +z/(a*b*log(c)*d*%e^(log(c)*d*z)+a^2*log(c)*d)$
6081
6082 /* Problem 788: OK */
6083 integrate(z^2/(b*c^(d*z)+a)^2,z);
6084 2*(-log(%e^(log(c)*d*z))^2*log(b*%e^(log(c)*d*z)/a+1)/2
6085   +li[3](-b*%e^(log(c)*d*z)/a)
6086   -log(%e^(log(c)*d*z))*li[2](-b*%e^(log(c)*d*z)/a))
6087  /(a^2*log(c)^3*d^3)
6088  +2*(log(%e^(log(c)*d*z))*log(b*%e^(log(c)*d*z)/a+1)
6089     +li[2](-b*%e^(log(c)*d*z)/a))
6090   /(a^2*log(c)^3*d^3)
6091  +(log(%e^(log(c)*d*z))^3-3*log(%e^(log(c)*d*z))^2)/(3*a^2*log(c)^3*d^3)
6092  +z^2/(a*b*log(c)*d*%e^(log(c)*d*z)+a^2*log(c)*d)$
6093
6094 /* Problem 789: OK */
6095 integrate(z^3/(b*c^(d*z)+a)^2,z);
6096 -6*(log(%e^(log(c)*d*z))^3*log(b*%e^(log(c)*d*z)/a+1)/6
6097    +li[4](-b*%e^(log(c)*d*z)/a)
6098    -log(%e^(log(c)*d*z))*li[3](-b*%e^(log(c)*d*z)/a)
6099    +log(%e^(log(c)*d*z))^2*li[2](-b*%e^(log(c)*d*z)/a)/2)
6100  /(a^2*log(c)^4*d^4)
6101  -6*(-log(%e^(log(c)*d*z))^2*log(b*%e^(log(c)*d*z)/a+1)/2
6102     +li[3](-b*%e^(log(c)*d*z)/a)
6103     -log(%e^(log(c)*d*z))*li[2](-b*%e^(log(c)*d*z)/a))
6104   /(a^2*log(c)^4*d^4)
6105  +(log(%e^(log(c)*d*z))^4-4*log(%e^(log(c)*d*z))^3)/(4*a^2*log(c)^4*d^4)
6106  +z^3/(a*b*log(c)*d*%e^(log(c)*d*z)+a^2*log(c)*d)$
6107
6108 /* Problem 790: OK */
6109 integrate(z^4/(b*c^(d*z)+a)^2,z);
6110 24*(-log(%e^(log(c)*d*z))^4*log(b*%e^(log(c)*d*z)/a+1)/24
6111    +li[5](-b*%e^(log(c)*d*z)/a)
6112    -log(%e^(log(c)*d*z))*li[4](-b*%e^(log(c)*d*z)/a)
6113    +log(%e^(log(c)*d*z))^2*li[3](-b*%e^(log(c)*d*z)/a)/2
6114    -log(%e^(log(c)*d*z))^3*li[2](-b*%e^(log(c)*d*z)/a)/6)
6115  /(a^2*log(c)^5*d^5)
6116  +24*(log(%e^(log(c)*d*z))^3*log(b*%e^(log(c)*d*z)/a+1)/6
6117      +li[4](-b*%e^(log(c)*d*z)/a)
6118      -log(%e^(log(c)*d*z))*li[3](-b*%e^(log(c)*d*z)/a)
6119      +log(%e^(log(c)*d*z))^2*li[2](-b*%e^(log(c)*d*z)/a)/2)
6120   /(a^2*log(c)^5*d^5)
6121  +(log(%e^(log(c)*d*z))^5-5*log(%e^(log(c)*d*z))^4)/(5*a^2*log(c)^5*d^5)
6122  +z^4/(a*b*log(c)*d*%e^(log(c)*d*z)+a^2*log(c)*d)$
6123
6124 /* ----- Involving z^n*%e^(c*z)/(a+b*%e^(c*z)) ------------------------------ */
6125
6126 /* Problem 791: NOUN */
6127 integrate(z*%e^(f*z)/(b*c^(d*z)+a),z);
6128 'integrate(z*%e^(f*z)/(b*c^(d*z)+a),z);
6129 /*  'integrate((a*(log(c)^2*d^2-log(c)*d*f)*z+a*log(c)*d)*%e^(f*z)
6130             /(b^2*(f^2-2*log(c)*d*f+log(c)^2*d^2)*%e^(2*log(c)*d*z)
6131              +a*b*(2*f^2-4*log(c)*d*f+2*log(c)^2*d^2)*%e^(log(c)*d*z)
6132              +a^2*(f^2-2*log(c)*d*f+log(c)^2*d^2)),z)
6133  -((log(c)*d-f)*z+1)*%e^(f*z)/(b*(f^2-2*log(c)*d*f+log(c)^2*d^2)
6134                                 *%e^(log(c)*d*z)
6135                               +a*(f^2-2*log(c)*d*f+log(c)^2*d^2));
6136 */
6137
6138 /* Problem 792: NOUN */
6139 integrate(z*%e^(d*z)/(b*%e^(c*z)+a),z);
6140 'integrate((a*(c^2-c*d)*z+a*c)*%e^(d*z)/(b^2*(d^2-2*c*d+c^2)*%e^(2*c*z)
6141                                         +a*b*(2*d^2-4*c*d+2*c^2)*%e^(c*z)
6142                                         +a^2*(d^2-2*c*d+c^2)),z)
6143  -((c-d)*z+1)*%e^(d*z)/(b*(d^2-2*c*d+c^2)*%e^(c*z)+a*(d^2-2*c*d+c^2));
6144
6145 /* Problem 793: OK */
6146 integrate(z*%e^(2*c*z)/(b*%e^(c*z)+a),z);
6147 -a*(log(%e^(c*z))*log(b*%e^(c*z)/a+1)+li[2](-b*%e^(c*z)/a))/(b^2*c^2)
6148  +a*log(%e^(c*z))^2/(2*b^2*c^2)+((2*b*c*z-2*b)*%e^(c*z)-a*c^2*z^2)/(2*b^2*c^2)$
6149
6150 /* Problem 794: OK */
6151 integrate(z*%e^-(2*c*z)/(b*%e^(c*z)+a),z);
6152 -b^2*(log(%e^(c*z))*log(b*%e^(c*z)/a+1)+li[2](-b*%e^(c*z)/a))/(a^3*c^2)
6153  +b^2*log(%e^(c*z))^2/(2*a^3*c^2)
6154  +((4*b*c*z+4*b)*%e^-(c*z)+(-2*a*c*z-a)*%e^-(2*c*z))/(4*a^2*c^2)$
6155
6156 /* Problem 795: OK */
6157 integrate(z*%e^(c*z)/(b*%e^(c*z)+a),z);
6158 (log(%e^(c*z))*log(b*%e^(c*z)/a+1)+li[2](-b*%e^(c*z)/a))/(b*c^2)
6159  -log(%e^(c*z))^2/(2*b*c^2)+z^2/(2*b)$
6160
6161 /* Problem 796: NOUN */
6162 integrate(z^2*%e^(f*z)/(b*c^(d*z)+a),z);
6163 'integrate(z^2*%e^(f*z)/(b*c^(d*z)+a),z);
6164 /* 'integrate((a*(log(c)*d*f^2-2*log(c)^2*d^2*f+log(c)^3*d^3)*z^2
6165             +a*(2*log(c)^2*d^2-2*log(c)*d*f)*z+2*a*log(c)*d)
6166             *%e^(f*z)
6167             /(b^2*(-f^3+3*log(c)*d*f^2-3*log(c)^2*d^2*f+log(c)^3*d^3)
6168                  *%e^(2*log(c)*d*z)
6169              +a*b*(-2*f^3+6*log(c)*d*f^2-6*log(c)^2*d^2*f+2*log(c)^3*d^3)
6170                *%e^(log(c)*d*z)
6171              +a^2*(-f^3+3*log(c)*d*f^2-3*log(c)^2*d^2*f+log(c)^3*d^3)),z)
6172  -((f^2-2*log(c)*d*f+log(c)^2*d^2)*z^2+(2*log(c)*d-2*f)*z+2)*%e^(f*z)
6173   /(b*(-f^3+3*log(c)*d*f^2-3*log(c)^2*d^2*f+log(c)^3*d^3)*%e^(log(c)*d*z)
6174    +a*(-f^3+3*log(c)*d*f^2-3*log(c)^2*d^2*f+log(c)^3*d^3));
6175 */
6176
6177 /* Problem 797: OK */
6178 integrate(z^2*%e^(c*z)/(b*%e^(c*z)+a),z);
6179 -2*(-log(%e^(c*z))^2*log(b*%e^(c*z)/a+1)/2
6180    +li[3](-b*%e^(c*z)/a)-log(%e^(c*z))*li[2](-b*%e^(c*z)/a))
6181  /(b*c^3)
6182  -log(%e^(c*z))^3/(3*b*c^3)+z^3/(3*b)$
6183
6184
6185 /* Problem 798: NOUN */
6186 integrate(z^3*%e^(f*z)/(b*c^(d*z)+a),z);
6187 'integrate(z^3*%e^(f*z)/(b*c^(d*z)+a),z);
6188 /* 'integrate((a*(-log(c)*d*f^3+3*log(c)^2*d^2*f^2-3*log(c)^3*d^3*f+log(c)^4*d^4)
6189              *z^3
6190             +a*(3*log(c)*d*f^2-6*log(c)^2*d^2*f+3*log(c)^3*d^3)*z^2
6191             +a*(6*log(c)^2*d^2-6*log(c)*d*f)*z+6*a*log(c)*d)
6192             *%e^(f*z)
6193             /(b^2*(f^4-4*log(c)*d*f^3+6*log(c)^2*d^2*f^2-4*log(c)^3*d^3*f
6194                       +log(c)^4*d^4)*%e^(2*log(c)*d*z)
6195              +a*b
6196                *(2*f^4-8*log(c)*d*f^3+12*log(c)^2*d^2*f^2-8*log(c)^3*d^3*f
6197                       +2*log(c)^4*d^4)*%e^(log(c)*d*z)
6198              +a^2*(f^4-4*log(c)*d*f^3+6*log(c)^2*d^2*f^2-4*log(c)^3*d^3*f
6199                       +log(c)^4*d^4)),z)
6200  -((-f^3+3*log(c)*d*f^2-3*log(c)^2*d^2*f+log(c)^3*d^3)*z^3
6201   +(3*f^2-6*log(c)*d*f+3*log(c)^2*d^2)*z^2+(6*log(c)*d-6*f)*z+6)
6202   *%e^(f*z)
6203   /(b*(f^4-4*log(c)*d*f^3+6*log(c)^2*d^2*f^2-4*log(c)^3*d^3*f+log(c)^4*d^4)
6204      *%e^(log(c)*d*z)
6205    +a*(f^4-4*log(c)*d*f^3+6*log(c)^2*d^2*f^2-4*log(c)^3*d^3*f+log(c)^4*d^4));
6206 */
6207
6208 /* Problem 799: OK */
6209 integrate(z^3*%e^(c*z)/(b*%e^(c*z)+a),z);
6210 6*(log(%e^(c*z))^3*log(b*%e^(c*z)/a+1)/6
6211   +li[4](-b*%e^(c*z)/a)-log(%e^(c*z))*li[3](-b*%e^(c*z)/a)
6212   +log(%e^(c*z))^2*li[2](-b*%e^(c*z)/a)/2)
6213  /(b*c^4)
6214  -log(%e^(c*z))^4/(4*b*c^4)+z^4/(4*b)$
6215
6216 /* Problem 800: OK */
6217 integrate(z^4*%e^(c*z)/(b*%e^(c*z)+a),z);
6218 -24*(-log(%e^(c*z))^4*log(b*%e^(c*z)/a+1)/24
6219     +li[5](-b*%e^(c*z)/a)-log(%e^(c*z))*li[4](-b*%e^(c*z)/a)
6220     +log(%e^(c*z))^2*li[3](-b*%e^(c*z)/a)/2
6221     -log(%e^(c*z))^3*li[2](-b*%e^(c*z)/a)/6)
6222  /(b*c^5)
6223  -log(%e^(c*z))^5/(5*b*c^5)+z^5/(5*b)$
6224
6225 /* ---- Involving z^n/(a*%e^(2*d*z)+b*%e^(d*z)+c) --------------------------- */
6226
6227 assume(4*a*c>b^2);
6228 [4*a*c>b^2];
6229
6230 /* Problem 802: NOUN */
6231 integrate(z/(c+b*%e^(d*z)+a*%e^(2*d*z)),z);
6232 'integrate(z/(a*%e^(2*d*z)+b*%e^(d*z)+c),z);
6233
6234 /* Problem 803: NOUN */
6235 integrate(z^2/(c+b*%e^(d*z)+a*%e^(2*d*z)),z);
6236 'integrate(z^2/(a*%e^(2*d*z)+b*%e^(d*z)+c),z);
6237
6238 /* Problem 804: NOUN */
6239 integrate(z^3/(c+b*%e^(d*z)+a*%e^(2*d*z)),z);
6240 'integrate(z^3/(a*%e^(2*d*z)+b*%e^(d*z)+c),z);
6241
6242 forget(4*a*c>b^2);
6243 [4*a*c>b^2];
6244
6245 /* ----- Involing z^n*(a+b*c^(d*z)^p ---------------------------------------- */
6246
6247 /* Problem 806: NOUN */
6248 integrate(z*(b*c^(d*z)+a)^p,z);
6249 'integrate((b*c^(d*z)+a)^p*z,z);
6250
6251 /* Problem 807: NOUN */
6252 integrate(z^2*(b*c^(d*z)+a)^p,z);
6253 'integrate((b*c^(d*z)+a)^p*z^2,z);
6254
6255 /* Problem 808: NOUN */
6256 integrate(z^3*(b*c^(d*z)+a)^p,z);
6257 'integrate((b*c^(d*z)+a)^p*z^3,z);
6258
6259 /* ----- Involing z^n*%e^(f*z)*(a+b*c^(d*z)^p ------------------------------- */
6260
6261 /* Problem 809: NOUN */
6262 integrate(z*%e^(f*z)*(b*c^(d*z)+a)^p,z);
6263 'integrate((b*c^(d*z)+a)^p*z*%e^(f*z),z);
6264
6265 /* Problem 810: NOUN */
6266 integrate(z^2*%e^(f*z)*(b*c^(d*z)+a)^p,z);
6267 'integrate((b*c^(d*z)+a)^p*z^2*%e^(f*z),z);
6268
6269 /* Problem 811: NOUN */
6270 integrate(z^3*%e^(f*z)*(b*c^(d*z)+a)^p,z);
6271 'integrate((b*c^(d*z)+a)^p*z^3*%e^(f*z),z);
6272
6273 /* Problem 812: NOUN */
6274 integrate(z^4*%e^(f*z)*(b*c^(d*z)+a)^p,z);
6275 'integrate((b*c^(d*z)+a)^p*z^4*%e^(f*z),z);
6276
6277 /* ----- End of file -------------------------------------------------------- */