Hyperbolic cosine integral: Integration (formula 01.20.21.2310)

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 cosh(c z))^nu)^beta

http://functions.wolfram.com/01.20.21.2310.01

Input Form

Integrate[((a + b Cosh[c z])^\[Nu])^\[Beta], z] == (1/(b c (1 + \[Beta] \[Nu]))) (AppellF1[1 + \[Beta] \[Nu], 1/2, 1/2, 2 + \[Beta] \[Nu], (a + b Cosh[c z])/(a + b), (a + b Cosh[c z])/(a - b)] Sqrt[(b (1 + Cosh[c z]))/(-a + b)] Sqrt[(b - b Cosh[c z])/(a + b)] (a + b Cosh[c z]) ((a + b Cosh[c z])^\[Nu])^\[Beta] Csch[c 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