Hyperbolic sine: Integration (formula 01.19.21.1403)

Sinh

$Mathematica Notation$

Elementary Functions

Sinh[z]

Integration

Indefinite integration

Involving one direct function and elementary functions

Involving trigonometric, exponential and a power functions

Involving cos, exp and power

Involving z^alpha-1e^{b z}cos(c z)sinh(a z)

http://functions.wolfram.com/01.19.21.1403.01

Input Form

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