Hyperbolic cosine integral: Integration (formula 01.20.21.0327)

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 z^alpha-1 e^{b z+e} cosh(c z)

http://functions.wolfram.com/01.20.21.0327.01

Input Form

Integrate[(E^(b z + e) Cosh[c z])/z^n, z] == (-E^(e + (-b + c) z)) (((-1)^n E^((b - c) z) ((-b - c) (-b + c)^n ExpIntegralEi[(b - c) z] - (-b - c)^n (b - c) ExpIntegralEi[(b + c) z]) + (-b - c)^n (b - c) E^(2 b z) (-1 + n)! Sum[((-b - c)^(k - n) z^(k - n))/Pochhammer[1 - n, k], {k, 1, -1 + n}] - (-b - c) (-b + c)^n E^(2 (b - c) z) (-1 + n)! Sum[((-b + c)^(k - n) z^(k - n))/Pochhammer[1 - n, k], {k, 1, -1 + n}])/ (2 (b^2 - c^2) (-1 + n)!)) /; Element[n, Integers] && n > 0

Standard Form

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MathML Form

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<apply> <times /> <cn type='integer'> -1 </cn> <ci> c </ci> </apply> </apply> <ci> n </ci> </apply> <apply> <plus /> <ci> b </ci> <apply> <times /> <cn type='integer'> -1 </cn> <ci> c </ci> </apply> </apply> <apply> <ci> ExpIntegralEi </ci> <apply> <times /> <apply> <plus /> <ci> b </ci> <ci> c </ci> </apply> <ci> z </ci> </apply> </apply> </apply> </apply> </apply> </apply> </apply> </apply> </apply> </apply> <apply> <in /> <ci> n </ci> <apply> <ci> SuperPlus </ci> <ci> ℕ </ci> </apply> </apply> </apply> </annotation-xml> </semantics> </math>

Rule Form

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Date Added to functions.wolfram.com (modification date)

2002-12-18