Hyperbolic cosine integral: Integration (formula 01.20.21.4761)

Cosh

$Mathematica Notation$

Elementary Functions

Cosh[z]

Integration

Indefinite integration

Involving functions of the direct function, hyperbolic and trigonometric functions

Involving rational functions of the direct function, hyperbolic and trigonometric functions

Involving sin and sinh

Involving sin(e z)(a sinh(c z)+b cosh(c z))^-n

http://functions.wolfram.com/01.20.21.4761.01

Input Form

Integrate[Sin[e z]/(a Sinh[c z] + b Cosh[c z])^2, z] == (1/(a - b)^2) (2 I ((1/(2 c - I e)) (E^((2 c - I e) z) Hypergeometric2F1[(2 c - I e)/(2 c), 2, (4 c - I e)/(2 c), ((a + b) E^(2 c z))/(a - b)]) - (1/(2 c + I e)) (E^((2 c + I e) z) Hypergeometric2F1[(2 c + I e)/(2 c), 2, (4 c + I e)/(2 c), ((a + b) E^(2 c z))/(a - b)])))

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