Hyperbolic cotangent: Integration (formula 01.22.21.0274)

Coth

$Mathematica Notation$

Elementary Functions

Coth[z]

Integration

Indefinite integration

Involving functions of the direct function

Involving algebraic functions of the direct function

Involving ((a+b coth²(c z))ⁿ)^beta

http://functions.wolfram.com/01.22.21.0274.01

Input Form

Integrate[((a + b Coth[c z]^2)^n)^\[Beta], z] == (1/c) ((AppellF1[1/2, 1, (-n) \[Beta], 3/2, Coth[c z]^2, -((b Coth[c z]^2)/a)] Coth[c z] ((a + b Coth[c z]^2)^n)^\[Beta])/ (1 + (b Coth[c z]^2)/a)^(n \[Beta]))

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