Hyperbolic sine: Integration (formula 01.19.21.2686)

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 powers of cos

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

http://functions.wolfram.com/01.19.21.2686.01

Input Form

Integrate[Cos[d + c z]^m Sinh[a z]^\[Nu], z] == (Sinh[a z]^\[Nu] ((1/(a \[Nu])) (Binomial[m, m/2] Hypergeometric2F1[ -(\[Nu]/2), -\[Nu], 1 - \[Nu]/2, E^(2 a z)] (-1 + Mod[m, 2])) - Sum[(Binomial[m, s] ((I E^(I (m - 2 s) (2 d + c z)) Hypergeometric2F1[ (I (c (m - 2 s) + I a \[Nu]))/(2 a), -\[Nu], (I c (m - 2 s) - a (-2 + \[Nu]))/(2 a), E^(2 a z)])/ (c (m - 2 s) + I a \[Nu]) + Hypergeometric2F1[-((I c (m - 2 s) + a \[Nu])/(2 a)), -\[Nu], -((I c (m - 2 s) + a (-2 + \[Nu]))/(2 a)), E^(2 a z)]/ E^(I c (m - 2 s) z)/(I c (m - 2 s) + a \[Nu])))/E^(I d (m - 2 s)), {s, 0, Floor[(1/2) (-1 + m)]}]))/(2^m (1 - E^(2 a z))^\[Nu]) /; Element[m, Integers] && m > 0

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