Hyperbolic cosine integral: Integration (formula 01.20.21.4387)

Cosh

$Mathematica Notation$

Elementary Functions

Cosh[z]

Integration

Indefinite integration

Involving functions of the direct function and hyperbolic functions

Involving algebraic functions of the direct function and hyperbolic functions

Involving rational functions of sinh

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

http://functions.wolfram.com/01.20.21.4387.01

Input Form

Integrate[1/((c + d Sinh[e z]) Sqrt[a + b Cosh[2 e z]]), z] == (Sqrt[(a + b Cosh[2 e z])/(a + b)] (-(ArcTanh[(Sqrt[1 + (2 b c^2)/((a + b) d^2)] Cosh[e z])/ (Sqrt[1 + c^2/d^2] Sqrt[(a + b Cosh[2 e z])/(a + b)])]/ (Sqrt[1 + c^2/d^2] Sqrt[1 + (2 b c^2)/((a + b) d^2)])) - (I d EllipticPi[-(d^2/c^2), I e z, (2 b)/(a + b)])/c))/ (d e Sqrt[a + b Cosh[2 e 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