Hyperbolic cosine integral: Integration (formula 01.20.21.2329)

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 cosh(c z))^nu)^beta cosh(d z)

http://functions.wolfram.com/01.20.21.2329.01

Input Form

Integrate[Sqrt[(a + b Cosh[c z])^3] Cosh[c z], z] == (Sqrt[(a + b Cosh[c z])^3] (-4 I (a^3 + a^2 b + 3 a b^2 + 3 b^3) Sqrt[(a + b Cosh[c z])/(a + b)] EllipticE[(I c z)/2, (2 b)/(a + b)] + 4 I a (a^2 - b^2) Sqrt[(a + b Cosh[c z])/(a + b)] EllipticF[(I c z)/2, (2 b)/(a + b)] + 2 b (4 a^2 + b^2 + 6 a b Cosh[c z] + b^2 Cosh[2 c z]) Sinh[c z]))/ (10 b c (a + b Cosh[c z])^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