Hyperbolic cosine integral: Integration (formula 01.20.21.2378)

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))^beta

http://functions.wolfram.com/01.20.21.2378.01

Input Form

Integrate[1/(a + b Cosh[c z]^2)^(5/2), z] == -(I (2 (a + b)^2 (2 a + b) ((2 a + b + b Cosh[2 c z])/(a + b))^(3/2) EllipticE[I c z, b/(a + b)] - a (a + b)^2 ((2 a + b + b Cosh[2 c z])/(a + b))^(3/2) EllipticF[I c z, b/(a + b)] - I Sqrt[2] b (5 a^2 + 5 a b + b^2 + b (2 a + b) Cosh[2 c z]) Sinh[2 c z]))/(3 a^2 (a + b)^2 c (2 a + b + b Cosh[2 c z])^(3/2))

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