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 Cot

 http://functions.wolfram.com/01.09.21.0144.01

 Input Form

 Integrate[E^(p z) Cos[b z]^m Cot[c z], z] == ((-I) Binomial[m, m/2] ((1/p) (E^(p z) HypergeometricPFQ[ {1, -((I p)/(2 c))}, {1 - (I p)/(2 c)}, E^(2 I c z)]) + (1/(2 I c + p)) (E^((2 I c + p) z) HypergeometricPFQ[ {1, 1 - (I p)/(2 c)}, {2 - (I p)/(2 c)}, E^(2 I c z)])) (1 - Mod[m, 2]))/2^m - (I Sum[Binomial[m, k] ((E^((I b (2 k - m) + p) z) HypergeometricPFQ[ {1, (b k)/c - (b m)/(2 c) - (I p)/(2 c)}, {1 + (b k)/c - (b m)/(2 c) - (I p)/(2 c)}, E^(2 I c z)])/ ((-I) b (-2 k + m) + p) + (E^((2 I c + I b (2 k - m) + p) z) HypergeometricPFQ[{1, 1 + (b k)/c - (b m)/(2 c) - (I p)/(2 c)}, {2 + (b k)/c - (b m)/(2 c) - (I p)/(2 c)}, E^(2 I c z)])/ (2 I c - I b (-2 k + m) + p) + (E^((-2 I b k + I b m + p) z) HypergeometricPFQ[{1, -((b k)/c) + (b m)/(2 c) - (I p)/(2 c)}, {1 - (b k)/c + (b m)/(2 c) - (I p)/(2 c)}, E^(2 I c z)])/ (I b (-2 k + m) + p) + (E^((2 I c - 2 I b k + I b m + p) z) HypergeometricPFQ[{1, 1 - (b k)/c + (b m)/(2 c) - (I p)/(2 c)}, {2 - (b k)/c + (b m)/(2 c) - (I p)/(2 c)}, E^(2 I c z)])/ (2 I c + I b (-2 k + m) + p)), {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