Hyperbolic cosine integral: Integration (formula 01.20.21.2313)

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

http://functions.wolfram.com/01.20.21.2313.01

Input Form

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

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