Hyperbolic cosine integral: Integration (formula 01.20.21.2395)

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))^nu)^beta

http://functions.wolfram.com/01.20.21.2395.01

Input Form

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