Hyperbolic sine: Integration (formula 01.19.21.1034)

Sinh

$Mathematica Notation$

Elementary Functions

Sinh[z]

Integration

Indefinite integration

Involving one direct function and elementary functions

Involving trigonometric and a power functions

Involving cos and power

Involving z^alpha-1cos(c z+d)sinh(a z+b)

http://functions.wolfram.com/01.19.21.1034.01

Input Form

Integrate[z^(\[Alpha] - 1) Cos[d + c z] Sinh[b + a z], z] == (1/4) E^(-b - I d) z^\[Alpha] (((-E^(2 b)) Gamma[\[Alpha], (-(a - I c)) z])/ ((-(a - I c)) z)^\[Alpha] + (E^(2 I d) Gamma[\[Alpha], (a - I c) z])/ ((a - I c) z)^\[Alpha] - (E^(2 b + 2 I d) Gamma[\[Alpha], (-(a + I c)) z])/ ((-(a + I c)) z)^\[Alpha] + Gamma[\[Alpha], (a + I c) z]/ ((a + I c) z)^\[Alpha])

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