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Exp






Mathematica Notation

Traditional Notation









Elementary Functions > Exp[z] > Integration > Indefinite integration > Involving functions of the direct function and a power function > Involving algebraic functions of the direct function and a power function > Involving zn(a+b cd z)beta





http://functions.wolfram.com/01.03.21.0794.01









  


  










Input Form





Integrate[z^3 (a + b c^(d z))^\[Beta], z] == (1/(d^4 \[Beta]^4 Log[c]^4)) (((a + b c^(d z))^\[Beta] (-6 HypergeometricPFQ[{-\[Beta], -\[Beta], -\[Beta], -\[Beta], -\[Beta]}, {1 - \[Beta], 1 - \[Beta], 1 - \[Beta], 1 - \[Beta]}, -(a/(c^(d z) b))] + d z \[Beta] Log[c] (6 HypergeometricPFQ[{-\[Beta], -\[Beta], -\[Beta], -\[Beta]}, {1 - \[Beta], 1 - \[Beta], 1 - \[Beta]}, -(a/(c^(d z) b))] + d z \[Beta] Log[c] (-3 HypergeometricPFQ[{-\[Beta], -\[Beta], -\[Beta]}, {1 - \[Beta], 1 - \[Beta]}, -(a/(c^(d z) b))] + d z \[Beta] Hypergeometric2F1[-\[Beta], -\[Beta], 1 - \[Beta], -(a/(c^(d z) b))] Log[c]))))/(1 + a/(c^(d z) b))^\[Beta])










Standard Form





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MathML Form







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</ci> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <ci> &#946; </ci> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <ci> &#946; </ci> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <ci> &#946; </ci> </apply> </list> <list> <apply> <plus /> <cn type='integer'> 1 </cn> <apply> <times /> <cn type='integer'> -1 </cn> <ci> &#946; </ci> </apply> </apply> <apply> <plus /> <cn type='integer'> 1 </cn> <apply> <times /> <cn type='integer'> -1 </cn> <ci> &#946; </ci> </apply> </apply> <apply> <plus /> <cn type='integer'> 1 </cn> <apply> <times /> <cn type='integer'> -1 </cn> <ci> &#946; </ci> </apply> </apply> </list> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <ci> a </ci> <apply> <power /> <ci> c </ci> <apply> <times /> <apply> <times /> <cn type='integer'> -1 </cn> <ci> d </ci> </apply> <ci> z </ci> </apply> </apply> <apply> <power /> <ci> b </ci> <cn type='integer'> -1 </cn> </apply> </apply> </apply> </apply> </apply> <apply> <times /> <ci> d </ci> <ci> z </ci> <ci> &#946; </ci> <apply> <ln /> <ci> c </ci> </apply> <apply> <plus /> <apply> <times /> <ci> d </ci> <ci> z </ci> <ci> &#946; </ci> <apply> <ci> Hypergeometric2F1 </ci> <apply> <times /> <cn type='integer'> -1 </cn> <ci> &#946; </ci> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <ci> &#946; </ci> </apply> <apply> <plus /> <cn type='integer'> 1 </cn> <apply> <times /> <cn type='integer'> -1 </cn> <ci> &#946; </ci> </apply> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <ci> a </ci> <apply> <power /> <ci> c </ci> <apply> <times /> <apply> <times /> <cn type='integer'> -1 </cn> <ci> d </ci> </apply> <ci> z </ci> </apply> </apply> <apply> <power /> <ci> b </ci> <cn type='integer'> -1 </cn> </apply> </apply> </apply> </apply> <apply> <ln /> <ci> c </ci> </apply> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <cn type='integer'> 3 </cn> <apply> <ci> HypergeometricPFQ </ci> <list> <apply> <times /> <cn type='integer'> -1 </cn> <ci> &#946; </ci> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <ci> &#946; </ci> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <ci> &#946; </ci> </apply> </list> <list> <apply> <plus /> <cn type='integer'> 1 </cn> <apply> <times /> <cn type='integer'> -1 </cn> <ci> &#946; </ci> </apply> </apply> <apply> <plus /> <cn type='integer'> 1 </cn> <apply> <times /> <cn type='integer'> -1 </cn> <ci> &#946; </ci> </apply> </apply> </list> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <ci> a </ci> <apply> <power /> <ci> c </ci> <apply> <times /> <apply> <times /> <cn type='integer'> -1 </cn> <ci> d </ci> </apply> <ci> z </ci> </apply> </apply> <apply> <power /> <ci> b </ci> <cn type='integer'> -1 </cn> </apply> </apply> </apply> </apply> </apply> </apply> </apply> </apply> </apply> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <cn type='integer'> 6 </cn> <apply> <ci> HypergeometricPFQ </ci> <list> <apply> <times /> <cn type='integer'> -1 </cn> <ci> &#946; </ci> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <ci> &#946; </ci> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <ci> &#946; </ci> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <ci> &#946; </ci> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <ci> &#946; </ci> </apply> </list> <list> <apply> <plus /> <cn type='integer'> 1 </cn> <apply> <times /> <cn type='integer'> -1 </cn> <ci> &#946; </ci> </apply> </apply> <apply> <plus /> <cn type='integer'> 1 </cn> <apply> <times /> <cn type='integer'> -1 </cn> <ci> &#946; </ci> </apply> </apply> <apply> <plus /> <cn type='integer'> 1 </cn> <apply> <times /> <cn type='integer'> -1 </cn> <ci> &#946; </ci> </apply> </apply> <apply> <plus /> <cn type='integer'> 1 </cn> <apply> <times /> <cn type='integer'> -1 </cn> <ci> &#946; </ci> </apply> </apply> </list> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <ci> a </ci> <apply> <power /> <ci> c </ci> <apply> <times /> <apply> <times /> <cn type='integer'> -1 </cn> <ci> d </ci> </apply> <ci> z </ci> </apply> </apply> <apply> <power /> <ci> b </ci> <cn type='integer'> -1 </cn> </apply> </apply> </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





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