Hyperbolic cosine integral: Integration (formula 01.20.21.1108)

Cosh

$Mathematica Notation$

Elementary Functions

Cosh[z]

Integration

Indefinite integration

Involving one direct function and elementary functions

Involving trigonometric and a power functions

Involving powers of cos and power

Involving z^alpha-1cos^mu(c z)cosh(a z+b)

http://functions.wolfram.com/01.20.21.1108.01

Input Form

Integrate[z^(\[Alpha] - 1) Cos[c z]^m Cosh[b + a z], z] == ((-2^(-1 - m)) z^\[Alpha] Binomial[m, m/2] (E^(2 b) ExpIntegralE[1 - \[Alpha], (-a) z] + ExpIntegralE[1 - \[Alpha], a z]) (1 - Mod[m, 2]))/E^b - (2^(-1 - m) z^\[Alpha] Sum[Binomial[m, s] (ExpIntegralE[1 - \[Alpha], (a + I c (m - 2 s)) z] + E^(2 b) ExpIntegralE[1 - \[Alpha], (-a + I c m - 2 I c s) z] + E^(2 b) ExpIntegralE[1 - \[Alpha], (-a - I c (m - 2 s)) z] + ExpIntegralE[1 - \[Alpha], (a - I c m + 2 I c s) z]), {s, 0, Floor[(1/2) (-1 + m)]}])/E^b /; 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