Hyperbolic cosine integral: Integration (formula 01.20.21.0857)

Cosh

$Mathematica Notation$

Elementary Functions

Cosh[z]

Integration

Indefinite integration

Involving one direct function and elementary functions

Involving trigonometric functions

Involving algebraic functions of cos

Involving (a+b cos(d z))^beta cosh(c z)

http://functions.wolfram.com/01.20.21.0857.01

Input Form

Integrate[(a + b Cos[d z])^\[Beta] Cosh[c z], z] == (1/(2 (c^2 + d^2 \[Beta]^2))) (((a + (1/2) b (E^((-I) d z) + E^(I d z)))^\[Beta] (E^(2 c z) (c + I d \[Beta]) AppellF1[-((I c)/d) - \[Beta], -\[Beta], -\[Beta], 1 - (I c)/d - \[Beta], -((b E^(I d z))/(a + Sqrt[a^2 - b^2])), (b E^(I d z))/ (-a + Sqrt[a^2 - b^2])] - (c - I d \[Beta]) AppellF1[(I c)/d - \[Beta], -\[Beta], -\[Beta], 1 + (I c)/d - \[Beta], -((b E^(I d z))/(a + Sqrt[a^2 - b^2])), (b E^(I d z))/ (-a + Sqrt[a^2 - b^2])]))/ (E^(c z) (1 + (b E^(I d z))/(a - Sqrt[a^2 - b^2]))^\[Beta] (1 + (b E^(I d z))/(a + Sqrt[a^2 - b^2]))^\[Beta]))

Standard Form

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MathML Form

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type='integer'> -1 </cn> </apply> </apply> </apply> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <apply> <plus /> <ci> c </ci> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <imaginaryi /> <ci> d </ci> <ci> β </ci> </apply> </apply> </apply> <apply> <ci> AppellF1 </ci> <apply> <plus /> <apply> <times /> <imaginaryi /> <ci> c </ci> <apply> <power /> <ci> d </ci> <cn type='integer'> -1 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <ci> β </ci> </apply> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <ci> β </ci> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <ci> β </ci> </apply> <apply> <plus /> <cn type='integer'> 1 </cn> <apply> <times /> <imaginaryi /> <ci> c </ci> <apply> <power /> <ci> d </ci> <cn type='integer'> -1 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <ci> β </ci> </apply> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <ci> b </ci> 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type='integer'> -1 </cn> <ci> a </ci> </apply> </apply> <cn type='integer'> -1 </cn> </apply> </apply> </apply> </apply> </apply> </apply> </apply> </apply> </annotation-xml> </semantics> </math>

Rule Form

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

2002-12-18