Hyperbolic cosine integral: Integration (formula 01.20.21.2373)

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/01.20.21.2373.01

Input Form

Integrate[(a + b Cosh[c z]^2)^(5/2), z] == (-16 I (23 a^3 + 46 a^2 b + 31 a b^2 + 8 b^3) Sqrt[(2 a + b + b Cosh[2 c z])/(a + b)] EllipticE[I c z, b/(a + b)] + 64 I a (2 a^2 + 3 a b + b^2) Sqrt[(2 a + b + b Cosh[2 c z])/(a + b)] EllipticF[I c z, b/(a + b)] + Sqrt[2] b (88 a^2 + 88 a b + 25 b^2 + 28 b (2 a + b) Cosh[2 c z] + 3 b^2 Cosh[4 c z]) Sinh[2 c z])/ (240 c 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