Cotangent: Integration (formula 01.09.21.0068)

Cot

$Mathematica Notation$

Elementary Functions

Cot[z]

Integration

Indefinite integration

Involving one direct function and elementary functions

Involving trigonometric functions

Involving cos

Involving cos(b z)

http://functions.wolfram.com/01.09.21.0068.01

Input Form

Integrate[Cos[b z] Cot[c z], z] == (1/(2 (b^3 - 4 b c^2))) ((b (b + 2 c) E^(I (b + 2 c) z) Hypergeometric2F1[1 - b/(2 c), 1, 2 - b/(2 c), E^(2 I c z)] - (b - 2 c) (b E^(I (3 b + 2 c) z) Hypergeometric2F1[1 + b/(2 c), 1, 2 + b/(2 c), E^(2 I c z)] + (b + 2 c) E^(I b z) (-Hypergeometric2F1[-(b/(2 c)), 1, 1 - b/(2 c), E^(2 I c z)] + E^(2 I b z) Hypergeometric2F1[b/(2 c), 1, 1 + b/(2 c), E^(2 I c z)])))/E^(2 I b z))

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