Hyperbolic cosine integral: Integration (formula 01.20.21.2433)

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/01.20.21.2433.01

Input Form

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

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