Cotangent: Integration (formula 01.09.21.0076)

Cot

$Mathematica Notation$

Elementary Functions

Cot[z]

Integration

Indefinite integration

Involving one direct function and elementary functions

Involving trigonometric functions

Involving power of cos

Involving cos^mu(b z)

http://functions.wolfram.com/01.09.21.0076.01

Input Form

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

Standard Form

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MathML Form

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Rule Form

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

2002-12-18