text: from sympy.core import Eq, Rational, Symbol
  from sympy.functions import sin, cos, tan, csc, sec, cot, log, Piecewise
  from sympy.integrals.trigonometry import trigintegrate
  
  x = Symbol('x')
  
  
  def test_trigintegrate_odd():
      assert trigintegrate(Rational(1), x) == x
      assert trigintegrate(x, x) is None
      assert trigintegrate(x**2, x) is None
  
      assert trigintegrate(sin(x), x) == -cos(x)
      assert trigintegrate(cos(x), x) == sin(x)
  
      assert trigintegrate(sin(3*x), x) == -cos(3*x)/3
      assert trigintegrate(cos(3*x), x) == sin(3*x)/3
  
      y = Symbol('y')
      assert trigintegrate(sin(y*x), x) == \
          Piecewise((0, Eq(y, 0)), (-cos(y*x)/y, True))
      assert trigintegrate(cos(y*x), x) == \
          Piecewise((x, Eq(y, 0)), (sin(y*x)/y, True))
      assert trigintegrate(sin(y*x)**2, x) == \
          Piecewise((0, Eq(y, 0)), ((x*y/2 - sin(x*y)*cos(x*y)/2)/y, True))
      assert trigintegrate(sin(y*x)*cos(y*x), x) == \
          Piecewise((0, Eq(y, 0)), (sin(x*y)**2/(2*y), True))
      assert trigintegrate(cos(y*x)**2, x) == \
          Piecewise((x, Eq(y, 0)), ((x*y/2 + sin(x*y)*cos(x*y)/2)/y, True))
  
      y = Symbol('y', positive=True)
      # TODO: remove conds='none' below. For this to work we would have to rule
      #       out (e.g. by trying solve) the condition y = 0, incompatible with
      #       y.is_positive being True.
      assert trigintegrate(sin(y*x), x, conds='none') == -cos(y*x)/y
      assert trigintegrate(cos(y*x), x, conds='none') == sin(y*x)/y
  
      assert trigintegrate(sin(x)*cos(x), x) == sin(x)**2/2
      assert trigintegrate(sin(x)*cos(x)**2, x) == -cos(x)**3/3
      assert trigintegrate(sin(x)**2*cos(x), x) == sin(x)**3/3
  
      # check if it selects right function to substitute,
      # so the result is kept simple
      assert trigintegrate(sin(x)**7 * cos(x), x) == sin(x)**8/8
      assert trigintegrate(sin(x) * cos(x)**7, x) == -cos(x)**8/8
  
      assert trigintegrate(sin(x)**7 * cos(x)**3, x) == \
          -sin(x)**10/10 + sin(x)**8/8
      assert trigintegrate(sin(x)**3 * cos(x)**7, x) == \
          cos(x)**10/10 - cos(x)**8/8
  
      # both n, m are odd and -ve, and not necessarily equal
      assert trigintegrate(sin(x)**-1*cos(x)**-1, x) == \
          -log(sin(x)**2 - 1)/2 + log(sin(x))
  
  
  def test_trigintegrate_even():
      assert trigintegrate(sin(x)**2, x) == x/2 - cos(x)*sin(x)/2
      assert trigintegrate(cos(x)**2, x) == x/2 + cos(x)*sin(x)/2
  
      assert trigintegrate(sin(3*x)**2, x) == x/2 - cos(3*x)*sin(3*x)/6
      assert trigintegrate(cos(3*x)**2, x) == x/2 + cos(3*x)*sin(3*x)/6
      assert trigintegrate(sin(x)**2 * cos(x)**2, x) == \
          x/8 - sin(2*x)*cos(2*x)/16
  
      assert trigintegrate(sin(x)**4 * cos(x)**2, x) == \
          x/16 - sin(x) *cos(x)/16 - sin(x)**3*cos(x)/24 + \
          sin(x)**5*cos(x)/6
  
      assert trigintegrate(sin(x)**2 * cos(x)**4, x) == \
          x/16 + cos(x) *sin(x)/16 + cos(x)**3*sin(x)/24 - \
          cos(x)**5*sin(x)/6
  
      assert trigintegrate(sin(x)**(-4), x) == -2*cos(x)/(3*sin(x)) \
          - cos(x)/(3*sin(x)**3)
  
      assert trigintegrate(cos(x)**(-6), x) == sin(x)/(5*cos(x)**5) \
          + 4*sin(x)/(15*cos(x)**3) + 8*sin(x)/(15*cos(x))
  
  
  def test_trigintegrate_mixed():
      assert trigintegrate(sin(x)*sec(x), x) == -log(cos(x))
      assert trigintegrate(sin(x)*csc(x), x) == x
      assert trigintegrate(sin(x)*cot(x), x) == sin(x)
  
      assert trigintegrate(cos(x)*sec(x), x) == x
      assert trigintegrate(cos(x)*csc(x), x) == log(sin(x))
      assert trigintegrate(cos(x)*tan(x), x) == -cos(x)
      assert trigintegrate(cos(x)*cot(x), x) == log(cos(x) - 1)/2 \
          - log(cos(x) + 1)/2 + cos(x)
      assert trigintegrate(cot(x)*cos(x)**2, x) == log(sin(x)) - sin(x)**2/2
  
  
  def test_trigintegrate_symbolic():
      n = Symbol('n', integer=True)
      assert trigintegrate(cos(x)**n, x) is None
      assert trigintegrate(sin(x)**n, x) is None
      assert trigintegrate(cot(x)**n, x) is None
  