Hyperbolic cosine integral: Integration (formula 06.40.21.0018)

CoshIntegral

$Mathematica Notation$

Gamma, Beta, Erf

CoshIntegral[z]

Integration

Indefinite integration

Involving one direct function and elementary functions

Involving exponential function and a power function

Involving exp and power

http://functions.wolfram.com/06.40.21.0018.01

Input Form

Integrate[z^2 E^(b z) CoshIntegral[a z], z] == (-(1/b^3)) ((-E^(b z)) (2 - 2 b z + b^2 z^2) CoshIntegral[a z] + ExpIntegralEi[(-a + b) z] + ExpIntegralEi[(a + b) z] + (1/((a - b)^2 (a + b)^2)) (b E^(b z) (b (a^2 (1 - b z) + b^2 (-3 + b z)) Cosh[a z] + a (b^2 (4 - b z) + a^2 (-2 + b z)) Sinh[a z])))

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)

2001-10-29