Hyperbolic cosine integral: Integration (formula 01.20.21.2425)

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 rational function of cosh(c z)

http://functions.wolfram.com/01.20.21.2425.01

Input Form

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