Hyperbolic cosine integral: Integration (formula 01.20.21.2340)

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))^betaand rational function of cosh(c z)

http://functions.wolfram.com/01.20.21.2340.01

Input Form

Integrate[(A + B Cosh[c z])/Sqrt[a + b Cosh[c z]], z] == -(2 I Sqrt[(a + b Cosh[c z])/(a + b)] ((a + b) B EllipticE[(I c z)/2, (2 b)/(a + b)] + (A b - a B) EllipticF[(I c z)/2, (2 b)/(a + b)]))/ (b c Sqrt[a + b Cosh[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