itest.cpp

   1 // For testing the integral function
   2
   3 #include "stdafx.h"
   4 #include "defs.h"
   5
   6 #if SELFTEST
   7
   8 static char *s[] = {
   9
  10         "clear",
  11         "",
  12
  13         "tty=1",
  14         "",
  15
  16         "integral(x^2+x)-(1/2*x^2+1/3*x^3)",
  17         "0",
  18
  19         "#1",
  20         "integral(A,X)",
  21         "A*X",
  22
  23         "#4",
  24         "integral(A+B,X)-(A*X+B*X)",
  25         "0",
  26
  27         "#9",
  28         "integral(1/X,X)",
  29         "log(X)",
  30
  31         "#11",
  32         "integral(exp(X),X)",
  33         "exp(X)",
  34
  35         "#12",
  36         "integral(exp(A*X),X)-exp(A*X)/A",
  37         "0",
  38
  39         "#14",
  40         "integral(log(X),X)-X*log(X)+X",
  41         "0",
  42
  43         "#15",
  44         "integral(3^X*log(3),X)",
  45         "3^X",
  46
  47         "#16",
  48         "integral(1/(3+x^2),x)-3^(-1/2)*arctan(3^(-1/2)*x)",
  49         "0",
  50
  51         "#17",
  52         "integral(1/(a-x^2),x)-a^(-1/2)*arctanh(a^(-1/2)*x)",
  53         "0",
  54
  55         "#19",
  56         "integral(1/sqrt(a-x^2),x)-arcsin(a^(-1/2)*x)",
  57         "0",
  58
  59         "#20",
  60         "integral(1/sqrt(a+x^2),x)-(log(x+(a+x^2)^(1/2)))",
  61         "0",
  62
  63         "#27",
  64         "integral(1/(a+b*x),x)-(log(a+b*x)/b)",
  65         "0",
  66
  67         "#28",
  68         "integral(1/(A+B*X)^2,X)+1/B*1/(A+B*X)",
  69         "0",
  70
  71         "#29",
  72         "integral(1/(a+b*x)^3,x)+1/2*1/b*(a+b*x)^(-2)",
  73         "0",
  74
  75         "#30",
  76         "integral(X/(A+B*X),X)+A*B^(-2)*log(A+B*X)-X/B",
  77         "0",
  78
  79         "#31",
  80         "integral(X/(A+B*X)^2,X)-1/B^2*(log(A+B*X)+A/(A+B*X))",
  81         "0",
  82
  83         "#33",
  84         "integral(X^2/(A+B*X),X)-1/B^2*(1/2*(A+B*X)^2-2*A*(A+B*X)+A^2*log(A+B*X))",
  85         "0",
  86
  87         "#34",
  88         "integral(X^2/(A+B*X)^2,X)-1/B^3*(A+B*X-2*A*log(A+B*X)-A^2/(A+B*X))",
  89         "0",
  90
  91         "#35",
  92         "integral(X^2/(A+B*X)^3,X)-1/B^3*(log(A+B*X)+2*A/(A+B*X)-1/2*A^2/(A+B*X)^2)",
  93         "0",
  94
  95         "#37",
  96         "integral(1/X*1/(A+B*X),X)+1/A*log((A+B*X)/X)",
  97         "0",
  98
  99         "#38",
 100         "integral(1/X*1/(A+B*X)^2,X)-1/A*1/(A+B*X)+1/A^2*log((A+B*X)/X)",
 101         "0",
 102
 103         "#39",
 104         "integral(1/X*1/(A+B*X)^3,X)-1/A^3*(1/2*((2*A+B*X)/(A+B*X))^2+log(X/(A+B*X)))",
 105         "0",
 106
 107         "#40",
 108         "integral(1/X^2*1/(A+B*X),X)+1/(A*X)-B/A^2*log((A+B*X)/X)",
 109         "0",
 110
 111         "#41",
 112         "integral(1/X^3*1/(A+B*X),X)-(2*B*X-A)/(2*A^2*X^2)-B^2/A^3*log(X/(A+B*X))",
 113         "0",
 114
 115         "#42",
 116         "integral(1/X^2*1/(A+B*X)^2,X)+(A+2*B*X)/(A^2*X*(A+B*X))-2*B/A^3*log((A+B*X)/X)",
 117         "0",
 118
 119         "#60",
 120         "integral(1/(2+3*X^2),X)-1/sqrt(6)*arctan(1/2*X*sqrt(6))",
 121         "0",
 122         "integral(1/(-2-3*X^2),X)-1/sqrt(6)*arctan(-1/2*X*sqrt(6))",
 123         "0",
 124
 125         "#61",
 126         "integral(1/(2-3*X^2),X)-1/2*1/sqrt(6)*log((2+X*sqrt(6))/(2-X*sqrt(6)))",
 127         "0",
 128         "integral(1/(-2+3*X^2),X)-1/2*1/sqrt(6)*log((-2+X*sqrt(6))/(-2-X*sqrt(6)))",
 129         "0",
 130
 131         "#63",
 132         "integral(X/(A+B*X^2),X)-1/2*1/B*log(A+B*X^2)",
 133         "0",
 134
 135         "#64",
 136         "integral(X^2/(A+B*X^2),X)-X/B+A/B*integral(1/(A+B*X^2),X)",
 137         "0",
 138
 139         "#65",
 140         "integral(1/(A+B*X^2)^2,X)-X/(2*A*(A+B*X^2))-1/2*1/A*integral(1/(A+B*X^2),X)",
 141         "0",
 142
 143         "#70",
 144         "integral(1/X*1/(A+B*X^2),X)-1/2*1/A*log(X^2/(A+B*X^2))",
 145         "0",
 146
 147         "#71",
 148         "integral(1/X^2*1/(A+B*X^2),X)+1/(A*X)+B/A*integral(1/(A+B*X^2),X)",
 149         "0",
 150
 151         "#74",
 152         "integral(1/(A+B*X^3),X)-1/3*1/A*(A/B)^(1/3)*(1/2*log(((A/B)^(1/3)+X)^3/(A+B*X^3))+sqrt(3)*arctan((2*X-(A/B)^(1/3))*(A/B)^(-1/3)/sqrt(3)))",
 153         "0",
 154
 155         "#76",
 156         "integral(X^2/(A+B*X^3),X)-1/3*1/B*log(A+B*X^3)",
 157         "0",
 158
 159         "#77",
 160         "integral(1/(2+3*X^4),X)-1/2*1/2*(2/3/4)^(1/4)*(1/2*log((X^2+2*(2/3/4)^(1/4)*X+2*(2/3/4)^(1/2))/(X^2-2*(2/3/4)^(1/4)*X+2*(2/3/4)^(1/2)))+arctan(2*(2/3/4)^(1/4)*X/(2*(2/3/4)^(1/2)-X^2)))",
 161         "0",
 162
 163         "#78",
 164         "integral(1/(2-3*X^4),X)-1/2*(2/3)^(1/4)/2*(1/2*log((X+(2/3)^(1/4))/(X-(2/3)^(1/4)))+arctan(X*(2/3)^(-1/4)))",
 165         "0",
 166
 167         "#79",
 168         "integral(X/(2+3*X^4),X)-1/2*1/3*1/sqrt(2/3)*arctan(X^2/sqrt(2/3))",
 169         "0",
 170
 171         "#80",
 172         "integral(X/(2-3*X^4),X)+1/4*1/3*sqrt(3/2)*log((X^2-sqrt(2/3))/(X^2+sqrt(2/3)))",
 173         "0",
 174
 175         "#81",
 176         "integral(X^2/(2+3*X^4),X)-1/4*1/3*(2/3/4)^(-1/4)*(1/2*log((X^2-2*(2/3/4)^(1/4)*X+2*sqrt(2/3/4))/(X^2+2*(2/3/4)^(1/4)*X+2*sqrt(2/3/4)))+arctan(2*(2/3/4)^(1/4)*X/(2*sqrt(2/3/4)-X^2)))",
 177         "0",
 178
 179         "#82",
 180         "integral(X^2/(2-3*X^4),X)+1/4*1/3*(2/3)^(-1/4)*(log((X-(2/3)^(1/4))/(X+(2/3)^(1/4)))+2*arctan(X*(2/3)^(-1/4)))",
 181         "0",
 182
 183         "#83",
 184         "integral(X^3/(A+B*X^4),X)-1/4*1/B*log(A+B*X^4)",
 185         "0",
 186
 187         "#124",
 188         "integral(sqrt(A+B*X),X)-2/3/B*sqrt((A+B*X)^3)",
 189         "0",
 190
 191         "#125",
 192         "integral(X*sqrt(A+B*X),X)+2*(2*A-3*B*X)*sqrt((A+B*X)^3)/15*B^(-2)",
 193         "0",
 194
 195         "#126",
 196         "integral(X^2*sqrt(A+B*X),X)-2*(8*A^2-12*A*B*X+15*B^2*X^2)*sqrt((A+B*X)^3)/105*B^(-3)",
 197         "0",
 198
 199         "#128",
 200         "integral(sqrt(A+B*X)/X,X)-2*sqrt(A+B*X)-A*integral(1/X*1/sqrt(A+B*X),X)",
 201         "0",
 202
 203         "#129",
 204         "integral(sqrt(A+B*X)/X^2,X)+sqrt(A+B*X)/X-B/2*integral(1/X*1/sqrt(A+B*X),X)",
 205         "0",
 206
 207         "#131",
 208         "integral(1/sqrt(A+B*X),X)-2*sqrt(A+B*X)/B",
 209         "0",
 210
 211         "#132",
 212         "integral(X/sqrt(A+B*X),X)+2/3*(2*A-B*X)*sqrt(A+B*X)/B^2",
 213         "0",
 214
 215         "#133",
 216         "integral(X^2/sqrt(A+B*X),X)-2/15*(8*A^2-4*A*B*X+3*B^2*X^2)*sqrt(A+B*X)/B^3",
 217         "0",
 218
 219         "#134",
 220         "integral(1/X*1/sqrt(2+B*X),X)-1/sqrt(2)*log((sqrt(2+B*X)-sqrt(2))/(sqrt(2+B*X)+sqrt(2)))",
 221         "0",
 222
 223         "#136",
 224         "integral(1/X*1/sqrt(-2+B*X),X)-2/sqrt(2)*arctan(sqrt((-2+B*X)/2))",
 225         "0",
 226
 227         "#137",
 228         "integral(1/X^2*1/sqrt(A+B*X),X)+sqrt(A+B*X)/A/X+1/2*B/A*integral(1/X*1/sqrt(A+B*X),X)",
 229         "0",
 230
 231         "#156",
 232         "integral(sqrt(X^2+A),X)-1/2*(X*sqrt(X^2+A)+A*log(X+sqrt(X^2+A)))",
 233         "0",
 234
 235         "#157",
 236         "integral(1/sqrt(X^2+A),X)-log(X+sqrt(X^2+A))",
 237         "0",
 238
 239         "#158",
 240         "integral(1/X*1/sqrt(X^2-2),X)-arcsec(X/sqrt(2))/sqrt(2)",
 241         "0",
 242
 243         "#159",
 244         "integral(1/X*1/sqrt(X^2+2),X)+1/sqrt(2)*log((sqrt(2)+sqrt(X^2+2))/X)",
 245         "0",
 246
 247         "#160",
 248         "integral(sqrt(X^2+2)/X,X)-sqrt(X^2+2)+sqrt(2)*log((sqrt(2)+sqrt(X^2+2))/X)",
 249         "0",
 250
 251         "#161",
 252         "integral(sqrt(X^2-2)/X,X)-sqrt(X^2-2)+sqrt(2)*arcsec(X/sqrt(2))",
 253         "0",
 254
 255         "#162",
 256         "integral(X/sqrt(X^2+A),X)-sqrt(X^2+A)",
 257         "0",
 258
 259         "#163",
 260         "integral(X*sqrt(X^2+A),X)-1/3*sqrt((X^2+A)^3)",
 261         "0",
 262
 263         "#164",
 264         "integral(sqrt((X^2+A)^3),X)-1/4*(X*sqrt((X^2+A)^3)+3/2*A*X*sqrt(X^2+A)+3/2*A^2*log(X+sqrt(X^2+A)))",
 265         "0",
 266 //      "integral(sqrt((X^2-A)^3),X)-1/4*(X*sqrt((X^2-A)^3)-3/2*A*X*sqrt(X^2-A)+3/2*A^2*log(X+sqrt(X^2-A)))",
 267 //      "0",
 268
 269         "#165",
 270         "integral(1/sqrt((X^2+A)^3),X)-X/A/sqrt(X^2+A)",
 271         "0",
 272
 273         "#166",
 274         "integral(X/sqrt((X^2+A)^3),X)+1/sqrt(X^2+A)",
 275         "0",
 276
 277         "#167",
 278         "integral(X*sqrt((X^2+A)^3),X)-1/5*sqrt((X^2+A)^5)",
 279         "0",
 280
 281         "#168",
 282         "integral(X^2*sqrt(X^2+A),X)-1/4*X*sqrt((X^2+A)^3)+1/8*A*X*sqrt(X^2+A)+1/8*A^2*log(X+sqrt(X^2+A))",
 283         "0",
 284
 285         "#169",
 286         "integral(X^3*sqrt(X^2+7),X)-(1/5*X^2-2/15*7)*sqrt((X^2+7)^3)",
 287         "0",
 288
 289         "#170",
 290         "integral(X^3*sqrt(X^2-7),X)-(sqrt((X^2-7)^5)/5+7*sqrt((X^2-7)^3)/3)",
 291         "0",
 292
 293         "#171",
 294         "integral(X^2/sqrt(X^2+A),X)-1/2*X*sqrt(X^2+A)+1/2*A*log(X+sqrt(X^2+A))",
 295         "0",
 296
 297         "#172",
 298         "integral(X^3/sqrt(X^2+A),X)-1/3*sqrt((X^2+A)^3)+A*sqrt(X^2+A)",
 299         "0",
 300
 301         "#173",
 302         "integral(1/X^2*1/sqrt(X^2+A),X)+sqrt(X^2+A)/A/X",
 303         "0",
 304
 305         "#174",
 306         "integral(1/X^3*1/sqrt(X^2+2),X)+1/2*sqrt(X^2+2)/2/X^2-1/2*log((sqrt(2)+sqrt(X^2+2))/X)/(sqrt(2)^3)",
 307         "0",
 308
 309         "#175",
 310         "integral(1/X^3*1/sqrt(X^2-2),X)-1/2*sqrt(X^2-2)/2/X^2-1/2*1/(2^(3/2))*arcsec(X/(2^(1/2)))",
 311         "0",
 312
 313         "#176+",
 314         "integral(X^2*sqrt((X^2+2^2)^3),X)"
 315         "-1/6*X*sqrt((X^2+2^2)^5)"
 316         "+1/24*(2^2)*X*sqrt((X^2+2^2)^3)"
 317         "+1/16*(2^4)X*sqrt(X^2+2^2)"
 318         "+1/16*(2^6)*log(X+sqrt(X^2+2^2))",
 319         "0",
 320
 321         "#176-",
 322         "integral(X^2*sqrt((X^2-2^2)^3),X)"
 323         "-1/6*X*sqrt((X^2-2^2)^5)"
 324         "-1/24*(2^2)*X*sqrt((X^2-2^2)^3)"
 325         "+1/16*(2^4)X*sqrt(X^2-2^2)"
 326         "-1/16*(2^6)*log(X+sqrt(X^2-2^2))",
 327         "0",
 328
 329         "#177+",
 330         "integral(X^3*sqrt((X^2+7^2)^3),X)"
 331         "-1/7*sqrt((X^2+7^2)^7)"
 332         "+1/5*(7^2)*sqrt((X^2+7^2)^5)",
 333         "0",
 334
 335         "#177-",
 336         "integral(X^3*sqrt((X^2-7^2)^3),X)"
 337         "-1/7*sqrt((X^2-7^2)^7)"
 338         "-1/5*(7^2)*sqrt((X^2-7^2)^5)",
 339         "0",
 340
 341         "#196",
 342         "simplify(integral(1/(X-A)/sqrt(X^2-A^2),X)+sqrt(X^2-A^2)/A/(X-A))",
 343         "0",
 344         "simplify(1/(X-A)/sqrt(X^2-A^2)-d(integral(1/(X-A)/sqrt(X^2-A^2),X),X))",
 345         "0",
 346
 347         "#197",
 348         "integral(1/(X+A)/sqrt(X^2-A^2),X)-sqrt(X^2-A^2)/A/(X+A)",
 349         "0",
 350         "simplify(1/(X+A)/sqrt(X^2-A^2)-d(integral(1/(X+A)/sqrt(X^2-A^2),X),X))",
 351         "0",
 352
 353         "#200",
 354         "integral(sqrt(7-X^2),X)-1/2*(X*sqrt(7-X^2)+7*arcsin(X/sqrt(7)))",
 355         "0",
 356
 357         "#201",
 358         "integral(1/sqrt(7-X^2),X)-arcsin(X/sqrt(7))",
 359         "0",
 360
 361         "#202",
 362         "integral(1/X*1/sqrt(7-X^2),X)+1/sqrt(7)*log((sqrt(7)+sqrt(7-X^2))/X)",
 363         "0",
 364
 365         "#203",
 366         "integral(sqrt(7-X^2)/X,X)"
 367         "-sqrt(7-X^2)+sqrt(7)*log((sqrt(7)+sqrt(7-X^2))/X)",
 368         "0",
 369
 370         "#204",
 371         "integral(X/sqrt(A-X^2),X)"
 372         "+sqrt(A-X^2)",
 373         "0",
 374
 375         "#205",
 376         "integral(X*sqrt(A-X^2),X)"
 377         "+1/3*sqrt((A-X^2)^3)",
 378         "0",
 379
 380         "#210",
 381         "integral(X^2*sqrt(7-X^2),X)"
 382         "+1/4*X*sqrt((7-X^2)^3)"
 383         "-7/8*(X*sqrt(7-X^2)+7*arcsin(X/sqrt(7)))",
 384         "0",
 385
 386         "#211",
 387         "integral(X^3*sqrt(7-X^2),X)"
 388         "-(-1/5*X^2-2/15*7)*sqrt((7-X^2)^3)",
 389         "0",
 390
 391         "#214",
 392         "integral(X^2/sqrt(7-X^2),X)"
 393         "+X/2*sqrt(7-X^2)"
 394         "-7/2*arcsin(X/sqrt(7))",
 395         "0",
 396
 397         "#215",
 398         "integral(1/X^2*1/sqrt(7-X^2),X)"
 399         "+sqrt(7-X^2)/7/X",
 400         "0",
 401
 402         "#216",
 403         "integral(sqrt(7-X^2)/X^2,X)"
 404         "+sqrt(7-X^2)/X"
 405         "+arcsin(X/sqrt(7))",
 406         "0",
 407
 408         "#217",
 409         "integral(sqrt(7-X^2)/X^3,X)"
 410         "+1/2*sqrt(7-X^2)/X^2"
 411         "-1/2*log((sqrt(7)+sqrt(7-X^2))/X)/sqrt(7)",
 412         "0",
 413
 414         "#218",
 415         "integral(sqrt(7-X^2)/X^4,X)"
 416         "+1/3*sqrt((7-X^2)^3)/7/X^3",
 417         "0",
 418
 419         "#273",
 420         "integral(sqrt(7*X^2+C),X)-X*sqrt(7*X^2+C)/2-C*log(X*sqrt(7)+sqrt(7*X^2+C))/2/sqrt(7)",
 421         "0",
 422
 423         "#274",
 424         "integral(sqrt(-7*X^2+C),X)-X*sqrt(-7*X^2+C)/2-C*arcsin(X*sqrt(7/C))/2/sqrt(7)",
 425         "0",
 426
 427         "#290",
 428         "integral(sin(A*X),X)+cos(A*X)/A",
 429         "0",
 430
 431         "#291",
 432         "integral(cos(A*X),X)-sin(A*X)/A",
 433         "0",
 434
 435         "#292",
 436         "integral(tan(A*X),X)+log(cos(A*X))/A",
 437         "0",
 438
 439         "#293",
 440         "integral(1/tan(A*X),X)-log(sin(A*X))/A",
 441         "0",
 442
 443         "#294",
 444         "integral(1/cos(A*X),X)-log(tan(pi/4+A*X/2))/A",
 445         "0",
 446
 447         "#295",
 448         "integral(1/sin(A*X),X)-log(tan(A*X/2))/A",
 449         "0",
 450
 451         "#296",
 452         "integral(sin(A*X)^2,X)-X/2+sin(2*A*X)/(4*A)",
 453         "0",
 454
 455         "#297",
 456         "integral(sin(A*X)^3,X)+cos(A*X)*(sin(A*X)^2+2)/(3*A)",
 457         "0",
 458
 459         "#298",
 460         "integral(sin(A*X)^4,X)-3/8*X+sin(2*A*X)/(4*A)-sin(4*A*X)/(32*A)",
 461         "0",
 462
 463         "#302",
 464         "integral(cos(A*X)^2,X)-X/2-sin(2*A*X)/(4*A)",
 465         "0",
 466
 467         "#303",
 468         "integral(cos(A*X)^3,X)-sin(A*X)*(cos(A*X)^2+2)/(3*A)",
 469         "0",
 470
 471         "#304",
 472         "integral(cos(A*X)^4,X)-3/8*X-sin(2*A*X)/(4*A)-sin(4*A*X)/(32*A)",
 473         "0",
 474
 475         "#308",
 476         "integral((1/sin(A*X))^2,X)+1/A*1/tan(A*X)",
 477         "0",
 478
 479         "#312",
 480         "integral((1/cos(A*X))^2,X)-tan(A*X)/A",
 481         "0",
 482
 483         "#318",
 484         "integral(sin(A*X)*cos(A*X),X)-sin(A*X)^2/(2*A)",
 485         "0",
 486
 487         "#320",
 488         "integral(sin(A*X)^2*cos(A*X)^2,X)+sin(4*A*X)/(32*A)-X/8",
 489         "0",
 490
 491         "#326",
 492         "integral(sin(A*X)/cos(A*X)/cos(A*X),X)-1/(A*cos(A*X))",
 493         "0",
 494
 495         "#327",
 496         "integral(sin(A*X)^2/cos(A*X),X)+sin(A*X)/A-log(tan(pi/4+A*X/2))/A",
 497         "0",
 498
 499         "#328",
 500         "integral(cos(A*X)/sin(A*X)^2,X)+1/(A*sin(A*X))",
 501         "0",
 502
 503         "#329",
 504         "integral(1/sin(A*X)/cos(A*X),X)-log(tan(A*X))/A",
 505         "0",
 506
 507         "#330",
 508         "integral(1/sin(A*X)/cos(A*X)^2,X)-(1/cos(A*X)+log(tan(A*X/2)))/A",
 509         "0",
 510
 511         "#332",
 512         "integral(1/sin(A*X)^2/cos(A*X),X)-(log(tan(pi/4+A*X/2))-1/sin(A*X))/A",
 513         "0",
 514
 515         "#333",
 516         "integral(1/sin(A*X)^2/cos(A*X)^2,X)+2/(A*tan(2*A*X))",
 517         "0",
 518
 519         "#335",
 520         "integral(sin(A+B*X),X)+cos(A+B*X)/B",
 521         "0",
 522
 523         "#336",
 524         "integral(cos(A+B*X),X)-sin(A+B*X)/B",
 525         "0",
 526
 527         "#337+",
 528         "integral(1/(1+sin(A*X)),X)+tan(pi/4-A*X/2)/A",
 529         "0",
 530
 531         "#337b+",
 532         "integral(1/(B+B*sin(A*X)),X)+tan(pi/4-A*X/2)/A/B",
 533         "0",
 534
 535         "#337-",
 536         "integral(1/(1-sin(A*X)),X)-tan(pi/4+A*X/2)/A",
 537         "0",
 538
 539         "#337b-",
 540         "integral(1/(B-B*sin(A*X)),X)-tan(pi/4+A*X/2)/A/B",
 541         "0",
 542
 543         "#338",
 544         "integral(1/(1+cos(A*X)),X)-tan(A*X/2)/A",
 545         "0",
 546
 547         "#339",
 548         "integral(1/(1-cos(A*X)),X)+1/(A*tan(A*X/2))",
 549         "0",
 550
 551         "#340",
 552         "integral(1/(A+B*sin(X)),X)-1/sqrt(B^2-A^2)*log((A*tan(X/2)+B-sqrt(B^2-A^2))/(A*tan(X/2)+B+sqrt(B^2-A^2)))",
 553         "0",
 554
 555         "#341",
 556         "integral(1/(A+B*cos(X)),X)-1/sqrt(B^2-A^2)*log((sqrt(B^2-A^2)*tan(X/2)+A+B)/(sqrt(B^2-A^2)*tan(X/2)-A-B))",
 557         "0",
 558
 559         "#389",
 560         "x*sin(A*x)-d(integral(x*sin(A*x)))",
 561         "0",
 562
 563         "#390",
 564         "x^2*sin(A*x)-d(integral(x^2*sin(A*x)))",
 565         "0",
 566
 567         "#393",
 568         "x*cos(A*x)-d(integral(x*cos(A*x)))",
 569         "0",
 570
 571         "#394",
 572         "x^2*cos(A*x)-d(integral(x^2*cos(A*x)))",
 573         "0",
 574
 575         "#441",
 576         "integral(arcsin(A*X),X)-X*arcsin(A*X)-sqrt(1-A^2*X^2)/A",
 577         "0",
 578
 579         "#442",
 580         "integral(arccos(A*X),X)-X*arccos(A*X)-sqrt(1-A^2*X^2)/A",
 581         "0",
 582
 583         "#443",
 584         "integral(arctan(A*X),X)-X*arctan(A*X)+log(1+A^2*X^2)/(2*A)",
 585         "0",
 586
 587         "#485",
 588         "integral(log(X),X)-X*log(X)+X",
 589         "0",
 590
 591         "#485a",
 592         "integral(log(A*X),X)-X*log(A*X)+X",
 593         "0",
 594
 595         "#486",
 596         "integral(X*log(X),X)-1/2*X^2*log(X)+1/4*X^2",
 597         "0",
 598
 599         "#486a",
 600         "integral(X*log(A*X),X)-1/2*X^2*log(A*X)+1/4*X^2",
 601         "0",
 602
 603         "#487",
 604         "integral(X^2*log(A*X),X)-1/3*X^3*log(A*X)+X^3/9",
 605         "0",
 606
 607         "#489",
 608         "integral(log(X)^2,X)-X*log(X)^2+2*X*log(X)-2*X",
 609         "0",
 610
 611         "#493",
 612         "integral(1/X*1/log(A*X),X)-log(log(A*X))",
 613         "0",
 614
 615         "#499",
 616         "integral(log(A*X+B),X)-(A*X+B)*log(A*X+B)/A+X",
 617         "0",
 618
 619         "#500",
 620         "integral(log(A*X+B)/X^2,X)-A*log(X)/B+(A*X+B)*log(A*X+B)/B/X",
 621         "0",
 622
 623         "#554",
 624         "integral(sinh(X),X)-cosh(X)",
 625         "0",
 626
 627         "#555",
 628         "integral(cosh(X),X)-sinh(X)",
 629         "0",
 630
 631         "#556",
 632         "integral(tanh(X),X)-log(cosh(X))",
 633         "0",
 634
 635         "#560",
 636         "integral(X*sinh(X),X)-X*cosh(X)+sinh(X)",
 637         "0",
 638
 639         "#562",
 640         "integral(X*cosh(X),X)-X*sinh(X)+cosh(X)",
 641         "0",
 642
 643         "#566",
 644         "integral(sinh(X)^2,X)-sinh(2*X)/4+X/2",
 645         "0",
 646
 647         "#569",
 648         "integral(tanh(X)^2,X)-X+tanh(X)",
 649         "0",
 650
 651         "#572",
 652         "integral(cosh(X)^2,X)-sinh(2*X)/4-X/2",
 653         "0",
 654
 655 // test integral(exp(a*x^2))
 656
 657         "integral(exp(a*x^2))+i*sqrt(pi)*erf(i*sqrt(a)*x)/sqrt(a)/2",
 658         "0",
 659
 660         "integral(exp(-x^2))-sqrt(pi)*erf(x)/2",
 661         "0",
 662
 663         "integral(exp(-3*x^2))-sqrt(pi/3)*erf(sqrt(3)*x)/2",
 664         "0",
 665
 666         "integral(1/x*1/(a+log(x)),x)-log(a+log(x))",
 667         "0",
 668
 669         "integral(exp(a*x+b*x))",
 670         "exp((a+b)*x)/(a+b)",
 671
 672         "integral(x*exp(a*x))",
 673         "-exp(a*x)/(a^2)+x*exp(a*x)/a",
 674         "derivative",
 675         "x*exp(a*x)",
 676
 677         "integral(x*exp(a*x+b))",
 678         "-exp(a*x+b)/(a^2)+x*exp(a*x+b)/a",
 679         "derivative",
 680         "x*exp(a*x+b)",
 681
 682         "integral(x*exp(-a*x+b))",
 683         "-exp(-a*x+b)/(a^2)-x*exp(-a*x+b)/a",
 684         "derivative",
 685         "x*exp(-a*x+b)",
 686
 687         "integral(x^2*exp(a*x))",
 688         "2*exp(a*x)/(a^3)-2*x*exp(a*x)/(a^2)+x^2*exp(a*x)/a",
 689         "derivative",
 690         "x^2*exp(a*x)",
 691
 692         "integral(x^2*exp(a*x+b))",
 693         "2*exp(a*x+b)/(a^3)-2*x*exp(a*x+b)/(a^2)+x^2*exp(a*x+b)/a",
 694         "derivative",
 695         "x^2*exp(a*x+b)",
 696
 697         "integral(x^3*exp(a*x))",
 698         "-6*exp(a*x)/(a^4)+6*x*exp(a*x)/(a^3)-3*x^2*exp(a*x)/(a^2)+x^3*exp(a*x)/a",
 699         "derivative",
 700         "x^3*exp(a*x)",
 701
 702         "integral(x^3*exp(a*x+b))",
 703         "-6*exp(a*x+b)/(a^4)+6*x*exp(a*x+b)/(a^3)-3*x^2*exp(a*x+b)/(a^2)+x^3*exp(a*x+b)/a",
 704         "derivative",
 705         "x^3*exp(a*x+b)",
 706
 707         "integral(sqrt(a*x^2+b))",
 708         "Stop: integral: sorry, could not find a solution",
 709
 710         "integral(x^2*(1-x^2)^(3/2))-(x*sqrt(1-x^2)*(-8*x^4+14*x^2-3)+3*arcsin(x))/48",
 711         "0",
 712
 713         "integral(x^4*(1-x^2)^(3/2))-(-x*sqrt(1-x^2)*(16*x^6-24*x^4+2*x^2+3)+3*arcsin(x))/128",
 714         "0",
 715
 716         "integral(x^2*(1-x^2)^(5/2))-(x*sqrt(1-x^2)*(48*x^6-136*x^4+118*x^2-15)+15*arcsin(x))/384",
 717         "0",
 718 };
 719
 720 void
 721 test_integral(void)
 722 {
 723         test(__FILE__, s, sizeof s / sizeof (char *));
 724 }
 725
 726 #endif