Hyperbolic cosine integral: Integration (formula 01.20.21.2406)

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 cosh^nu(c z)

http://functions.wolfram.com/01.20.21.2406.01

Input Form

Integrate[(a + b Cosh[c z]^2)^(3/2) Cosh[c z]^4, z] == (1/(1120 b^2 c)) (Sqrt[2 a + b + b Cosh[2 c z]] ((32 I (2 (a^3 - 2 a^2 b - 12 a b^2 - 8 b^3) EllipticE[I c z, b/(a + b)] + a (-2 a^2 + 5 a b + 8 b^2) EllipticF[I c z, b/(a + b)]))/ Sqrt[(2 a + b + b Cosh[2 c z])/(a + b)] + Sqrt[2] b (8 a^2 + 120 a b + 103 b^2 + 4 b (8 a + 11 b) Cosh[2 c z] + 5 b^2 Cosh[4 c z]) Sinh[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