Hyperbolic cosine integral: Integration (formula 01.20.21.1285)

Cosh

$Mathematica Notation$

Elementary Functions

Cosh[z]

Integration

Indefinite integration

Involving one direct function and elementary functions

Involving trigonometric and exponential functions

Involving powers of cos and exp

Involving e^{p z}cos^mu(c z) cosh(a z+b)

http://functions.wolfram.com/01.20.21.1285.01

Input Form

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