Exponential function: Integration (formula 01.03.21.0519)

Exp

$Mathematica Notation$

Elementary Functions

Exp[z]

Integration

Indefinite integration

Involving functions of the direct function

Involving algebraic functions of the direct function

Involving e^{e z} (a e^{2d z}+b e^{d z}+c)^beta

http://functions.wolfram.com/01.03.21.0519.01

Input Form

Integrate[E^(e z) (a E^(2 d z) + b E^(d z) + c)^\[Beta], z] == (1/e) ((E^(e z) (c + b E^(d z) + a E^(2 d z))^\[Beta] AppellF1[e/d, -\[Beta], -\[Beta], 1 + e/d, -((2 a E^(d z))/(b + Sqrt[b^2 - 4 a c])), (2 a E^(d z))/(-b + Sqrt[b^2 - 4 a c])])/ ((1 - (2 a E^(d z))/(-b + Sqrt[b^2 - 4 a c]))^\[Beta] (1 + (2 a E^(d z))/(b + Sqrt[b^2 - 4 a c]))^\[Beta]))

Standard Form

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MathML Form

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type='integer'> 4 </cn> <ci> a </ci> <ci> c </ci> </apply> </apply> </apply> <cn type='rational'> 1 <sep /> 2 </cn> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <ci> b </ci> </apply> </apply> <cn type='integer'> -1 </cn> </apply> </apply> </apply> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <ci> β </ci> </apply> </apply> <apply> <power /> <apply> <plus /> <apply> <times /> <cn type='integer'> 2 </cn> <apply> <power /> <exponentiale /> <apply> <times /> <ci> d </ci> <ci> z </ci> </apply> </apply> <ci> a </ci> <apply> <power /> <apply> <plus /> <ci> b </ci> <apply> <power /> <apply> <plus /> <apply> <power /> <ci> b </ci> <cn type='integer'> 2 </cn> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <cn type='integer'> 4 </cn> <ci> a </ci> <ci> c </ci> </apply> </apply> </apply> <cn type='rational'> 1 <sep /> 2 </cn> </apply> </apply> <cn type='integer'> -1 </cn> </apply> </apply> <cn type='integer'> 1 </cn> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <ci> β </ci> </apply> </apply> <apply> <power /> <apply> <plus /> <apply> <times /> <apply> <power /> <exponentiale /> <apply> <times /> <cn type='integer'> 2 </cn> <ci> d </ci> <ci> z </ci> </apply> </apply> <ci> a </ci> </apply> <apply> <times /> <ci> b </ci> <apply> <power /> <exponentiale /> <apply> <times /> <ci> d </ci> <ci> z </ci> </apply> </apply> </apply> <ci> c </ci> </apply> <ci> β </ci> </apply> <apply> <ci> AppellF1 </ci> <apply> <times /> <ci> e </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> <times /> <cn type='integer'> -1 </cn> <ci> β </ci> </apply> <apply> <plus /> <apply> <times /> <ci> e </ci> <apply> <power /> <ci> d </ci> <cn type='integer'> -1 </cn> </apply> </apply> <cn type='integer'> 1 </cn> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <cn type='integer'> 2 </cn> <ci> a </ci> <apply> <power /> 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Rule Form

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

2002-12-18