Hyperbolic sine: Integration (formula 01.19.21.0876)

Sinh

$Mathematica Notation$

Elementary Functions

Sinh[z]

Integration

Indefinite integration

Involving one direct function and elementary functions

Involving trigonometric functions

Involving cot

http://functions.wolfram.com/01.19.21.0876.01

Input Form

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

Standard Form

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MathML Form

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<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> <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> </annotation-xml> </semantics> </math>

Rule Form

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

2002-12-18