sympy/integrals/tests/test_integrals.py

   1 from sympy import symbols, integrate, exp, oo, Symbol, Rational, log
   2 from sympy.utilities.pytest import XFAIL
   3 import py
   4
   5 x,a,t = symbols('xat')
   6
   7 def test_improper_integral():
   8     assert integrate(log(x), (x, 0, 1)) == -1
   9     assert integrate(x**(-2), (x, 1, oo)) == 1
  10
  11
  12 def diff(expr, sym):
  13     from sympy.core import Derivative
  14     if isinstance(sym, Symbol):
  15         return Derivative(expr, sym)
  16     else:
  17         return Derivative(expr, sym[0]==[sym[1], sym[2]])
  18
  19
  20 def test_basics():
  21     e=(t+1)**2
  22     assert integrate(e, (t,0,x), evaluate=False).diff(x)==((1+x)**2).expand()
  23     assert integrate(e, (t,0,x), evaluate=False).diff(a)==0
  24
  25     assert integrate(e, (t,a,x), evaluate=False).diff(x)==((1+x)**2).expand()
  26     assert integrate(e, (t,x,a), evaluate=False).diff(x)==(-(1+x)**2).expand()
  27
  28     assert integrate(t**2, (t,x,2*x), evaluate=False).diff(x)==7*x**2
  29
  30 @XFAIL
  31 def test_unevaluated():
  32     py.test.raises(IntegralError,"integrate(e, (t,0,x), evaluate=False).diff(t)")
  33     py.test.raises(IntegralError,"integrate(e, t, evaluate=False).diff(x)")
  34
  35
  36
  37 def test_integration():
  38     assert integrate(0, (t,0,x)) == 0
  39     assert integrate(3, (t,0,x)) == 3*x
  40     assert integrate(t, (t,0,x)) == x**2/2
  41     assert integrate(3*t, (t,0,x))== 3*x**2/2
  42     assert integrate(3*t**2, (t,0,x)) == x**3
  43     assert integrate(1/t, (t,1,x)) == log(x)
  44     assert integrate(-1/t**2, (t,1,x)) == 1/x-1
  45     assert integrate(t**2+5*t-8, (t,0,x)) == x**3/3+5*x**2/2-8*x
  46     assert integrate(x**2, x) == x**3/3
  47     assert integrate((3*t*x)**5, x) == (3*t)**5 * x**6 / 6
  48
  49     b = Symbol("b")
  50     c = Symbol("c")
  51     assert integrate(a*t, (t,0,x))==a*x**2/2
  52     assert integrate(a*t**4, (t,0,x))==a*x**5/5
  53     assert integrate(a*t**2+b*t+c, (t,0,x))==a*x**3/3+b*x**2/2+c*x
  54
  55 def test_multiple_integration():
  56     y = Symbol('y')
  57     assert integrate((x**2)*(y**2), (x,0,1), (y,-1,2)) == Rational(1)
  58     assert integrate((y**2)*(x**2), x, y) == Rational(1,9)*(x**3)*(y**3)
  59
  60
  61 def test_issue433():
  62     assert integrate(exp(-x), (x,0,oo)) == 1
  63
  64 def test_issue461():
  65     assert integrate(x**Rational(3,2), x) == 2*x**Rational(5,2)/5
  66     assert integrate(x**Rational(1,2), x) == 2*x**Rational(3,2)/3
  67     assert integrate(x**Rational(-3,2), x) == -2*x**Rational(-1,2)
  68