Hyperbolic cosine integral: Integration (formula 01.20.21.1056)

Cosh

$Mathematica Notation$

Elementary Functions

Cosh[z]

Integration

Indefinite integration

Involving one direct function and elementary functions

Involving trigonometric and a power functions

Involving cos and power

Involving z^alpha-1 cos(b z^r) cosh(c z^r)

http://functions.wolfram.com/01.20.21.1056.01

Input Form

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

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