Hyperbolic cosine integral: Integration (formula 01.20.21.0366)

Cosh

$Mathematica Notation$

Elementary Functions

Cosh[z]

Integration

Indefinite integration

Involving one direct function and elementary functions

Involving exponential function and a power function

Involving exp and power

Involving zⁿ e^{b z^r+e} cosh(f z+g)

http://functions.wolfram.com/01.20.21.0366.01

Input Form

Integrate[z^n E^(b z^2 + e) Cosh[f z + g], z] == (-(1/4)) b^(-1 - n) (E^(e - f^2/(4 b) - g) Sum[2^(-n + q) f^(n - q) (-f + 2 b z)^(1 + q) (-((-f + 2 b z)^2/b))^ ((1/2) (-1 - q)) Binomial[n, q] Gamma[(1 + q)/2, -((-f + 2 b z)^2/(4 b))], {q, 0, n}] + E^(e - f^2/(4 b) + g) Sum[2^(-n + q) (-f)^(n - q) (f + 2 b z)^(1 + q) (-((f + 2 b z)^2/b))^ ((1/2) (-1 - q)) Binomial[n, q] Gamma[(1 + q)/2, -((f + 2 b z)^2/(4 b))], {q, 0, n}]) /; Element[n, Integers] && n >= 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