Hyperbolic cosine integral: Integration (formula 01.20.21.0775)

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)cosh(a z+b)

http://functions.wolfram.com/01.20.21.0775.01

Input Form

Integrate[Cos[c z]^m Cosh[b + a z], z] == (Binomial[m, m/2] (1 - Mod[m, 2]) Sinh[b + a z])/(2^m a) + Sum[Binomial[m, j] ((Cosh[(a + 2 I c j - I c m) z] Sinh[b])/ (a + 2 I c j - I c m) + (Cosh[(a - 2 I c j + I c m) z] Sinh[b])/ (a - 2 I c j + I c m) + (Cosh[b] Sinh[(a + 2 I c j - I c m) z])/ (a + 2 I c j - I c m) + (Cosh[b] Sinh[(a - 2 I c j + I c m) z])/ (a - 2 I c j + I c m)), {j, 0, Floor[(1/2) (-1 + m)]}]/2^m /; Element[m, Integers] && m > 0

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