Hyperbolic cosine integral: Integration (formula 01.20.21.0876)

Cosh

$Mathematica Notation$

Elementary Functions

Cosh[z]

Integration

Indefinite integration

Involving one direct function and elementary functions

Involving trigonometric functions

Involving tan

http://functions.wolfram.com/01.20.21.0876.01

Input Form

Integrate[Tan[b z] Cosh[c z], z] == (1/(2 (c^3 + 4 c b^2))) ((I ((-c) (c - 2 I b) E^(2 (c + I b) z) Hypergeometric2F1[1 - (I c)/(2 b), 1, 2 - (I c)/(2 b), -E^(2 I b z)] + (c + 2 I b) (c E^(2 I b z) Hypergeometric2F1[1 + (I c)/(2 b), 1, 2 + (I c)/(2 b), -E^(2 I b z)] + (c - 2 I b) (E^(2 c z) Hypergeometric2F1[ -((I c)/(2 b)), 1, 1 - (I c)/(2 b), -E^(2 I b z)] - Hypergeometric2F1[(I c)/(2 b), 1, 1 + (I c)/(2 b), -E^(2 I b z)]))))/ E^(c z))

Standard Form

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MathML Form

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<apply> <plus /> <cn type='integer'> 1 </cn> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <imaginaryi /> <ci> c </ci> <apply> <power /> <apply> <times /> <cn type='integer'> 2 </cn> <ci> b </ci> </apply> <cn type='integer'> -1 </cn> </apply> </apply> </apply> </apply> <cn type='integer'> 1 </cn> <apply> <plus /> <cn type='integer'> 2 </cn> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <imaginaryi /> <ci> c </ci> <apply> <power /> <apply> <times /> <cn type='integer'> 2 </cn> <ci> b </ci> </apply> <cn type='integer'> -1 </cn> </apply> </apply> </apply> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <power /> <exponentiale /> <apply> <times /> <cn type='integer'> 2 </cn> <imaginaryi /> <ci> b </ci> <ci> z </ci> </apply> </apply> </apply> </apply> </apply> </apply> </apply> </apply> </apply> </apply> </annotation-xml> </semantics> </math>

Rule Form

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

2002-12-18