Hyperbolic sine: Integration (formula 01.19.21.1842)

Sinh

$Mathematica Notation$

Elementary Functions

Sinh[z]

Integration

Indefinite integration

Involving functions of the direct function and a power function

Involving powers of the direct function and a power function

Involving powers of sinh and power

Involving z^alpha-1 sinh^v(a z)

http://functions.wolfram.com/01.19.21.1842.01

Input Form

Integrate[z Sinh[a z]^\[Nu], z] == (1/(a^2 (1 + \[Nu]))) (2^(-2 - \[Nu]) Sinh[a z]^(1 + \[Nu]) (2^(2 + \[Nu]) a z Cosh[a z] Hypergeometric2F1[1, (2 + \[Nu])/2, (3 + \[Nu])/2, -Sinh[a z]^2] - Sqrt[Pi] (1 + \[Nu]) Gamma[1 + \[Nu]] HypergeometricPFQRegularized[{1, (2 + \[Nu])/2, (2 + \[Nu])/2}, {(3 + \[Nu])/2, (4 + \[Nu])/2}, -Sinh[a z]^2] Sinh[a z]))

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