Hyperbolic cosine integral: Integration (formula 01.20.21.4356)

Cosh

$Mathematica Notation$

Elementary Functions

Cosh[z]

Integration

Indefinite integration

Involving functions of the direct function and hyperbolic functions

Involving algebraic functions of the direct function and hyperbolic functions

Involving sinh

Involving sinh^m(c z)cosh^m(c z)(a+b cosh(2c z))^beta

http://functions.wolfram.com/01.20.21.4356.01

Input Form

Integrate[(Sinh[c z]^2 Cosh[c z]^4)/Sqrt[a + b Cosh[2 c z]], z] == (-4 I (4 a^3 - a^2 b - 8 a b^2 - 3 b^3) Sqrt[(a + b Cosh[2 c z])/(a + b)] EllipticE[I c z, (2 b)/(a + b)] + 4 I (4 a^3 - 5 a^2 b - 4 a b^2 + 5 b^3) Sqrt[(a + b Cosh[2 c z])/(a + b)] EllipticF[I c z, (2 b)/(a + b)] + b (-8 a^2 + 10 a b + 3 b^2 - 2 (a - 5 b) b Cosh[2 c z] + 3 b^2 Cosh[4 c z]) Sinh[2 c z])/(240 b^3 c Sqrt[a + b Cosh[2 c z]])

Standard Form

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MathML Form

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<apply> <power /> <apply> <plus /> <ci> a </ci> <ci> b </ci> </apply> <cn type='integer'> -1 </cn> </apply> </apply> </apply> </apply> <apply> <times /> <cn type='integer'> 4 </cn> <imaginaryi /> <apply> <plus /> <apply> <times /> <cn type='integer'> 4 </cn> <apply> <power /> <ci> a </ci> <cn type='integer'> 3 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <cn type='integer'> 5 </cn> <ci> b </ci> <apply> <power /> <ci> a </ci> <cn type='integer'> 2 </cn> </apply> </apply> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <cn type='integer'> 4 </cn> <apply> <power /> <ci> b </ci> <cn type='integer'> 2 </cn> </apply> <ci> a </ci> </apply> </apply> <apply> <times /> <cn type='integer'> 5 </cn> <apply> <power /> <ci> b </ci> <cn type='integer'> 3 </cn> </apply> </apply> </apply> <apply> <power /> <apply> <times /> <apply> <plus /> <ci> a </ci> <apply> <times /> <ci> b </ci> <apply> <cosh /> <apply> <times /> <cn 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Rule Form

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Date Added to functions.wolfram.com (modification date)

2002-12-18