Hyperbolic cosine integral: Integration (formula 01.20.21.2437)

Cosh

$Mathematica Notation$

Elementary Functions

Cosh[z]

Integration

Indefinite integration

Involving functions of the direct function

Involving algebraic functions of the direct function

Other integrals

http://functions.wolfram.com/01.20.21.2437.01

Input Form

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