Hyperbolic cosine integral: Integration (formula 01.20.21.2314)

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/01.20.21.2314.01

Input Form

Integrate[1/Sqrt[(a + b Cosh[c z])^5], z] == (-((1/(a - b)^2) (2 I (a + b) ((a + b Cosh[c z])/(a + b))^(5/2) (4 a EllipticE[(I c z)/2, (2 b)/(a + b)] + (-a + b) EllipticF[(I c z)/2, (2 b)/(a + b)]))) + (1/(a^2 - b^2)^2) (2 b (a + b Cosh[c z]) (-5 a^2 + b^2 - 4 a b Cosh[c z]) Sinh[c z]))/(3 c Sqrt[(a + b Cosh[c z])^5])

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