Hyperbolic sine: Integration (formula 01.19.21.2606)

Sinh

$Mathematica Notation$

Elementary Functions

Sinh[z]

Integration

Indefinite integration

Involving functions of the direct function and trigonometric functions

Involving powers of the direct function and trigonometric functions

Involving cos

Involving cos(c z+d)sinh^v(a z)

http://functions.wolfram.com/01.19.21.2606.01

Input Form

Integrate[Cos[d + c z] Sinh[a z]^\[Nu], z] == ((-(1/2)) ((1/(c + I a \[Nu])) (I E^(I (2 d + c z)) Hypergeometric2F1[(I (c + I a \[Nu]))/(2 a), -\[Nu], (I c - a (-2 + \[Nu]))/(2 a), E^(2 a z)]) + (1/(I c + a \[Nu])) (Hypergeometric2F1[-((I c + a \[Nu])/(2 a)), -\[Nu], -((I c + a (-2 + \[Nu]))/(2 a)), E^(2 a z)]/E^(I c z))) Sinh[a z]^\[Nu])/(E^(I d) (1 - E^(2 a z))^\[Nu])

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