Hyperbolic sine: Integration (formula 01.19.21.1349)

Sinh

$Mathematica Notation$

Elementary Functions

Sinh[z]

Integration

Indefinite integration

Involving one direct function and elementary functions

Involving trigonometric and exponential functions

Involving sec and exp

http://functions.wolfram.com/01.19.21.1349.01

Input Form

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

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