tests/integrals/test_trigonometry.py

1 from diofant import (Eq, Integer, Piecewise, Symbol, cos, cot, csc, log, sec,
15     assert trigintegrate(sin(x), x) == -cos(x)
16     assert trigintegrate(cos(x), x) == sin(x)
18     assert trigintegrate(sin(3*x), x) == -cos(3*x)/3
19     assert trigintegrate(cos(3*x), x) == sin(3*x)/3
23         Piecewise((0, Eq(y, 0)), (-cos(y*x)/y, True))
24     assert trigintegrate(cos(y*x), x) == \
27         Piecewise((0, Eq(y, 0)), ((x*y/2 - sin(x*y)*cos(x*y)/2)/y, True))
29         (x*y/2 - sin(x*y)*cos(x*y)/2)/y
30     assert trigintegrate(sin(y*x)*cos(y*x), x) == \
32     assert trigintegrate(cos(y*x)**2, x) == \
33         Piecewise((x, Eq(y, 0)), ((x*y/2 + sin(x*y)*cos(x*y)/2)/y, True))
39     assert trigintegrate(sin(y*x), x, conds='none') == -cos(y*x)/y
40     assert trigintegrate(cos(y*x), x, conds='none') == sin(y*x)/y
42     assert trigintegrate(sin(x)*cos(x), x) == sin(x)**2/2
43     assert trigintegrate(sin(x)*cos(x)**2, x) == -cos(x)**3/3
44     assert trigintegrate(sin(x)**2*cos(x), x) == sin(x)**3/3
48     assert trigintegrate(sin(x)**7 * cos(x), x) == sin(x)**8/8
49     assert trigintegrate(sin(x) * cos(x)**7, x) == -cos(x)**8/8
51     assert trigintegrate(sin(x)**7 * cos(x)**3, x) == \
53     assert trigintegrate(sin(x)**3 * cos(x)**7, x) == \
54         cos(x)**10/10 - cos(x)**8/8
58     assert trigintegrate(sin(x)**2, x) == x/2 - cos(x)*sin(x)/2
59     assert trigintegrate(cos(x)**2, x) == x/2 + cos(x)*sin(x)/2
61     assert trigintegrate(sin(3*x)**2, x) == x/2 - cos(3*x)*sin(3*x)/6
62     assert trigintegrate(cos(3*x)**2, x) == x/2 + cos(3*x)*sin(3*x)/6
63     assert trigintegrate(sin(x)**2 * cos(x)**2, x) == \
64         x/8 - sin(2*x)*cos(2*x)/16
66     assert trigintegrate(sin(x)**4 * cos(x)**2, x) == \
67         x/16 - sin(x) * cos(x)/16 - sin(x)**3*cos(x)/24 + \
68         sin(x)**5*cos(x)/6
70     assert trigintegrate(sin(x)**2 * cos(x)**4, x) == \
71         x/16 + cos(x) * sin(x)/16 + cos(x)**3*sin(x)/24 - \
72         cos(x)**5*sin(x)/6
74     assert trigintegrate(sin(x)**(-4), x) == -2*cos(x)/(3*sin(x)) \
75         - cos(x)/(3*sin(x)**3)
77     assert trigintegrate(cos(x)**(-6), x) == sin(x)/(5*cos(x)**5) \
78         + 4*sin(x)/(15*cos(x)**3) + 8*sin(x)/(15*cos(x))
80     assert trigintegrate(sin(x)**4/cos(x)**2, x) == \
81         -3*x/2 + sin(x)**3/cos(x) + 3*sin(x)*cos(x)/2
82     assert trigintegrate(cos(x)**4/sin(x)**2, x) == \
83         -3*x/2 - 3*sin(x)*cos(x)/2 - cos(x)**3/sin(x)
84     assert trigintegrate(sin(x)**2/cos(x)**2, x) == -x + sin(x)/cos(x)
85     assert trigintegrate(sin(x)**-2*cos(x)**2, x) == -x - cos(x)/sin(x)
93     assert trigintegrate(cos(x)*sec(x), x) == x
94     assert trigintegrate(cos(x)*csc(x), x) == log(cos(x)**2 - 1)/2
95     assert trigintegrate(cos(x)*tan(x), x) == -cos(x)
96     assert trigintegrate(cos(x)*cot(x), x) == log(cos(x) - 1)/2 \
97         - log(cos(x) + 1)/2 + cos(x)
102     assert trigintegrate(cos(x)**n, x) is None