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 Cot

 http://functions.wolfram.com/01.09.21.0138.01

 Input Form

 Integrate[E^(p z) Sin[b z]^m Cot[c z], z] == -((1/((2 c - I p) p)) ((Binomial[m, m/2] (E^(p z) (2 I c + p) Hypergeometric2F1[-((I p)/(2 c)), 1, 1 - (I p)/(2 c), E^(2 I c z)] + E^((2 I c + p) z) p Hypergeometric2F1[1 - (I p)/(2 c), 1, 2 - (I p)/(2 c), E^(2 I c z)]) (1 - Mod[m, 2]))/2^m)) - Sum[(-1)^k Binomial[m, k] (E^((I m Pi)/2) ((E^((2 I c - I b (-2 k + m) + p) z) ((-I) b (-2 k + m) + p) Hypergeometric2F1[(2 c + 2 b k - b m - I p)/(2 c), 1, (4 c + 2 b k - b m - I p)/(2 c), E^(2 I c z)] + E^(((-I) b (-2 k + m) + p) z) (2 I c - I b (-2 k + m) + p) Hypergeometric2F1[-((b (-2 k + m) + I p)/(2 c)), 1, (2 c + 2 b k - b m - I p)/(2 c), E^(2 I c z)])/ ((2 c + 2 b k - b m - I p) (I b (2 k - m) + p))) + (E^((2 I c + I b (-2 k + m) + p) z) (I b (-2 k + m) + p) Hypergeometric2F1[(2 c - 2 b k + b m - I p)/(2 c), 1, (4 c - 2 b k + b m - I p)/(2 c), E^(2 I c z)] + E^((I b (-2 k + m) + p) z) (2 I c + I b (-2 k + m) + p) Hypergeometric2F1[(b (-2 k + m) - I p)/(2 c), 1, (2 c - 2 b k + b m - I p)/(2 c), E^(2 I c z)])/ ((2 c + b (-2 k + m) - I p) (I b (-2 k + m) + p))/E^((1/2) I m Pi)), {k, 0, Floor[(1/2) (-1 + m)]}]/2^m /; Element[m, Integers] && m > 0

 Standard Form

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 MathML Form

 Rule Form

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 Date Added to functions.wolfram.com (modification date)

 2002-12-18