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Sinh






Mathematica Notation

Traditional Notation









Elementary Functions > Sinh[z] > Integration > Indefinite integration > Involving one direct function and elementary functions > Involving power function > Involving power > Involving zalpha-1and arguments a zr





http://functions.wolfram.com/01.19.21.0097.01









  


  










Input Form





Integrate[z^n Sinh[a Sqrt[z]], z] == (-(ExpIntegralEi[(-a) Sqrt[z]]/(-2 - 2 n)!) + ExpIntegralEi[a Sqrt[z]]/ (-2 - 2 n)! - E^(a Sqrt[z]) Sum[((-a) Sqrt[z])^k/ Pochhammer[2 + 2 n, -1 + k - 2 n], {k, 0, 1 + 2 n}] + E^(a Sqrt[z]) Sum[((-a) Sqrt[z])^k/Pochhammer[2 + 2 n, -1 + k - 2 n], {k, 2 + 2 n, -1}] + Sum[(a Sqrt[z])^k/Pochhammer[2 + 2 n, -1 + k - 2 n], {k, 0, 1 + 2 n}]/ E^(a Sqrt[z]) - Sum[(a Sqrt[z])^k/Pochhammer[2 + 2 n, -1 + k - 2 n], {k, 2 + 2 n, -1}]/E^(a Sqrt[z]))/a^(2 (1 + n)) /; Element[n, Integers]










Standard Form





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MathML Form







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</ci> <apply> <plus /> <apply> <times /> <cn type='integer'> 2 </cn> <ci> n </ci> </apply> <cn type='integer'> 2 </cn> </apply> <apply> <plus /> <ci> k </ci> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <cn type='integer'> 2 </cn> <ci> n </ci> </apply> </apply> <cn type='integer'> -1 </cn> </apply> </apply> <cn type='integer'> -1 </cn> </apply> </apply> </apply> </apply> </apply> <apply> <times /> <apply> <ci> ExpIntegralEi </ci> <apply> <times /> <ci> a </ci> <apply> <power /> <ci> z </ci> <cn type='rational'> 1 <sep /> 2 </cn> </apply> </apply> </apply> <apply> <power /> <apply> <factorial /> <apply> <plus /> <apply> <times /> <cn type='integer'> -2 </cn> <ci> n </ci> </apply> <cn type='integer'> -2 </cn> </apply> </apply> <cn type='integer'> -1 </cn> </apply> </apply> </apply> </apply> </apply> <apply> <in /> <ci> n </ci> <integers /> </apply> </apply> </annotation-xml> </semantics> </math>










Rule Form





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





2002-12-18