Hyperbolic cosine integral: Integration (formula 01.20.21.2432)

Cosh

$Mathematica Notation$

Elementary Functions

Cosh[z]

Integration

Indefinite integration

Involving functions of the direct function

Involving algebraic functions of the direct function

Involving (a+b cosh²(c z))^betaand algebraic function of cosh(c z)

http://functions.wolfram.com/01.20.21.2432.01

Input Form

Integrate[(a + b Cosh[c z]^2)^\[Nu] (d + e Cosh[c z]^2)^\[Beta] Cosh[c z], z] == (1/c) ((AppellF1[1/2, -\[Nu], -\[Beta], 3/2, -((b Sinh[c z]^2)/(a + b)), -((e Sinh[c z]^2)/(d + e))] (a + b Cosh[c z]^2)^\[Nu] (d + e Cosh[c z]^2)^\[Beta] Sinh[c z])/ (((a + b Cosh[c z]^2)/(a + b))^\[Nu] ((d + e Cosh[c z]^2)/(d + e))^ \[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