Hyperbolic cosine integral: Integration (formula 01.20.21.1808)

Cosh

$Mathematica Notation$

Elementary Functions

Cosh[z]

Integration

Indefinite integration

Involving one direct function and elementary functions

Involving hyperbolic and a power functions

Involving products of sinh and power

Involving z^alpha-1sinh(a z) sinh(b z) cosh(c z)

http://functions.wolfram.com/01.20.21.1808.01

Input Form

Integrate[z^(\[Alpha] - 1) Sinh[a z] Sinh[b z] Cosh[c z], z] == (1/8) z^\[Alpha] ((-((-(a + b - c)) z)^(-\[Alpha])) Gamma[\[Alpha], (-(a + b - c)) z] - Gamma[\[Alpha], (a + b - c) z]/ ((a + b - c) z)^\[Alpha] + Gamma[\[Alpha], (-(a - b + c)) z]/ ((-(a - b + c)) z)^\[Alpha] + Gamma[\[Alpha], (a - b + c) z]/ ((a - b + c) z)^\[Alpha] + Gamma[\[Alpha], (-(-a + b + c)) z]/ ((-(-a + b + c)) z)^\[Alpha] + Gamma[\[Alpha], (-a + b + c) z]/ ((-a + b + c) z)^\[Alpha] - Gamma[\[Alpha], (-(a + b + c)) z]/ ((-(a + b + c)) z)^\[Alpha] - Gamma[\[Alpha], (a + b + c) z]/ ((a + b + c) z)^\[Alpha])

Standard Form

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MathML Form

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<times /> <cn type='integer'> -1 </cn> <apply> <plus /> <ci> a </ci> <ci> b </ci> <ci> c </ci> </apply> </apply> <ci> z </ci> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <ci> α </ci> </apply> </apply> <apply> <ci> Gamma </ci> <ci> α </ci> <apply> <times /> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <plus /> <ci> a </ci> <ci> b </ci> <ci> c </ci> </apply> </apply> <ci> z </ci> </apply> </apply> </apply> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <apply> <power /> <apply> <times /> <apply> <plus /> <ci> a </ci> <ci> b </ci> <ci> c </ci> </apply> <ci> z </ci> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <ci> α </ci> </apply> </apply> <apply> <ci> Gamma </ci> <ci> α </ci> <apply> <times /> <apply> <plus /> <ci> a </ci> <ci> b </ci> <ci> c </ci> </apply> <ci> z </ci> </apply> </apply> </apply> </apply> </apply> </apply> </apply> </annotation-xml> </semantics> </math>

Rule Form

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

2002-12-18