def test_manualintegrate_trigonometry():
    assert manualintegrate(sin(x), x) == -cos(x)
    assert manualintegrate(tan(x), x) == -log(cos(x))

    assert manualintegrate(sec(x), x) == log(sec(x) + tan(x))
    assert manualintegrate(csc(x), x) == -log(csc(x) + cot(x))

    assert manualintegrate(sin(x) * cos(x), x) in [sin(x) ** 2 / 2, -cos(x)**2 / 2]
    assert manualintegrate(-sec(x) * tan(x), x) == -sec(x)
    assert manualintegrate(csc(x) * cot(x), x) == -csc(x)
    assert manualintegrate(sec(x)**2, x) == tan(x)
    assert manualintegrate(csc(x)**2, x) == -cot(x)

    assert manualintegrate(x * sec(x**2), x) == log(tan(x**2) + sec(x**2))/2
    assert manualintegrate(cos(x)*csc(sin(x)), x) == -log(cot(sin(x)) + csc(sin(x)))
dataset/ETHPy150Open sympy/sympy/sympy/integrals/tests/test_manual.py/test_manualintegrate_trigonometry/original