Hyperbolic cosecant: Integration (formula 01.23.21.0123)

Csch

$Mathematica Notation$

Elementary Functions

Csch[z]

Integration

Indefinite integration

Involving one direct function and elementary functions

Involving hyperbolic functions

Involving algebraic functions of cosh

Involving (a+b cosh(c z))^beta

http://functions.wolfram.com/01.23.21.0123.01

Input Form

Integrate[(a + b Cosh[c z])^\[Beta] Csch[c z], z] == ((a + b Cosh[c z])^(1 + \[Beta]) ((a + b) Hypergeometric2F1[1 + \[Beta], 1, 2 + \[Beta], (a + b Cosh[c z])/(a - b)] + (-a + b) Hypergeometric2F1[1 + \[Beta], 1, 2 + \[Beta], (a + b Cosh[c z])/(a + b)]))/ (2 (a - b) (a + b) c (1 + \[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