Hyperbolic cosine integral: Integration (formula 01.20.21.0776)

Cosh

$Mathematica Notation$

Elementary Functions

Cosh[z]

Integration

Indefinite integration

Involving one direct function and elementary functions

Involving trigonometric functions

Involving powers of cos

Involving cos^mu(c z+d)cosh(a z+b)

http://functions.wolfram.com/01.20.21.0776.01

Input Form

Integrate[Cos[d + c z]^\[Mu] Cosh[b + a z], z] == ((1/2) Cos[d + c z]^\[Mu] (-((1/(a + I c \[Mu])) (Hypergeometric2F1[(I (a + I c \[Mu]))/(2 c), -\[Mu], 1 + (I a)/(2 c) - \[Mu]/2, -E^(2 I (d + c z))]/E^(a z))) + (1/(a - I c \[Mu])) (E^(2 b + a z) Hypergeometric2F1[ -((I a + c \[Mu])/(2 c)), -\[Mu], 1 - (I a)/(2 c) - \[Mu]/2, -E^(2 I (d + c z))])))/(E^b (1 + E^(2 I (d + c z)))^\[Mu])

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