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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+e sinh(c z)





http://functions.wolfram.com/01.19.21.0326.01









  


  










Input Form





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










Standard Form





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MathML Form







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<cn type='integer'> -1 </cn> <ci> b </ci> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <ci> c </ci> </apply> </apply> <ci> n </ci> </apply> </apply> <apply> <times /> <apply> <power /> <apply> <plus /> <ci> c </ci> <apply> <times /> <cn type='integer'> -1 </cn> <ci> b </ci> </apply> </apply> <ci> n </ci> </apply> <apply> <ci> ExpIntegralEi </ci> <apply> <times /> <apply> <plus /> <ci> b </ci> <apply> <times /> <cn type='integer'> -1 </cn> <ci> c </ci> </apply> </apply> <ci> z </ci> </apply> </apply> <apply> <plus /> <apply> <times /> <cn type='integer'> -1 </cn> <ci> b </ci> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <ci> c </ci> </apply> </apply> </apply> </apply> </apply> </apply> </apply> </apply> </apply> <apply> <in /> <ci> n </ci> <apply> <ci> SuperPlus </ci> <ci> &#8469; </ci> </apply> </apply> </apply> </annotation-xml> </semantics> </math>










Rule Form





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





2002-12-18