Hyperbolic cosine integral: Integration (formula 01.20.21.1150)

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-1 cos^m(b z^r+e) cosh(c z^r+g)

http://functions.wolfram.com/01.20.21.1150.01

Input Form

Integrate[z^n Cos[b z^2 + e]^m Cosh[c z^2 + g], z] == (-2^(-2 - m)) z^(1 + n) Binomial[m, m/2] (E^g ((-c) z^2)^((1/2) (-1 - n)) Gamma[(1 + n)/2, (-c) z^2] + ((c z^2)^((1/2) (-1 - n)) Gamma[(1 + n)/2, c z^2])/E^g) (1 - Mod[m, 2]) - 2^(-2 - m) z^(1 + n) Sum[Binomial[m, k] (E^(g - 2 I e k + I e m) ((-c + 2 I b k - I b m) z^2)^ ((1/2) (-1 - n)) Gamma[(1 + n)/2, (-c + 2 I b k - I b m) z^2] + E^(-g - 2 I e k + I e m) ((c + 2 I b k - I b m) z^2)^((1/2) (-1 - n)) Gamma[(1 + n)/2, (c + 2 I b k - I b m) z^2] + E^(g + 2 I e k - I e m) ((-c - 2 I b k + I b m) z^2)^((1/2) (-1 - n)) Gamma[(1 + n)/2, (-c - 2 I b k + I b m) z^2] + E^(-g + 2 I e k - I e m) ((c - 2 I b k + I b m) z^2)^((1/2) (-1 - n)) Gamma[(1 + n)/2, (c - 2 I b k + I b m) z^2]), {k, 0, Floor[(1/2) (-1 + m)]}] /; Element[n, Integers] && n >= 0 && 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