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Sinh






Mathematica Notation

Traditional Notation









Elementary Functions > Sinh[z] > Integration > Indefinite integration > Involving one direct function and elementary functions > Involving exponential function and a power function > Involving exp and power > Involving zalpha-1 eb z sinh(c z+d)





http://functions.wolfram.com/01.19.21.0348.01









  


  










Input Form





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










Standard Form





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MathML Form







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<ci> Pochhammer </ci> <apply> <plus /> <ci> n </ci> <cn type='integer'> 1 </cn> </apply> <apply> <plus /> <ci> k </ci> <apply> <times /> <cn type='integer'> -1 </cn> <ci> n </ci> </apply> </apply> </apply> <cn type='integer'> -1 </cn> </apply> </apply> </apply> </apply> </apply> </apply> </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