Hyperbolic sine: Integration (formula 01.19.21.2607)

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/01.19.21.2607.01

Input Form

Integrate[Cos[d + c z] Sinh[a z]^v, z] == (-2^(-1 - v)) ((2 E^((I Pi v)/2) Binomial[v, v/2] (-1 + Mod[v, 2]) Sin[d + c z])/c + Sum[((-1)^k (E^(((-I) c + a (-2 k + v)) z)/(I c + a (2 k - v)) + E^(2 I d + I Pi v + (I c + a (2 k - v)) z)/((-I) c + a (-2 k + v)) + E^(I Pi v - I c z + 2 a k z - a v z)/(I c + a (-2 k + v)) - E^(2 I d + (I c + a (-2 k + v)) z)/(I c + a (-2 k + v))) Binomial[v, k])/E^(I d), {k, 0, Floor[(1/2) (-1 + v)]}]) /; Element[v, Integers] && v > 0

Standard Form

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MathML Form

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</annotation-xml> </semantics> </math>

Rule Form

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Date Added to functions.wolfram.com (modification date)

2002-12-18