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Sin






Mathematica Notation

Traditional Notation









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





http://functions.wolfram.com/01.06.21.0476.01









  


  










Input Form





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










Standard Form





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MathML Form







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</ci> </bvar> <lowlimit> <apply> <times /> <cn type='integer'> 2 </cn> <apply> <plus /> <ci> n </ci> <cn type='integer'> 1 </cn> </apply> </apply> </lowlimit> <uplimit> <cn type='integer'> -1 </cn> </uplimit> <apply> <times /> <apply> <power /> <apply> <times /> <apply> <plus /> <apply> <times /> <cn type='integer'> -1 </cn> <ci> b </ci> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <imaginaryi /> <ci> c </ci> </apply> </apply> </apply> <apply> <power /> <ci> z </ci> <cn type='rational'> 1 <sep /> 2 </cn> </apply> </apply> <ci> k </ci> </apply> <apply> <power /> <apply> <ci> Pochhammer </ci> <apply> <times /> <cn type='integer'> 2 </cn> <apply> <plus /> <ci> n </ci> <cn type='integer'> 1 </cn> </apply> </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> 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type='rational'> 1 <sep /> 2 </cn> </apply> </apply> </apply> <apply> <power /> <apply> <factorial /> <apply> <times /> <cn type='integer'> -2 </cn> <apply> <plus /> <ci> n </ci> <cn type='integer'> 1 </cn> </apply> </apply> </apply> <cn type='integer'> -1 </cn> </apply> </apply> </apply> <apply> <times /> <apply> <power /> <exponentiale /> <apply> <times /> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <plus /> <apply> <times /> <imaginaryi /> <ci> c </ci> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <ci> b </ci> </apply> </apply> </apply> <apply> <power /> <ci> z </ci> <cn type='rational'> 1 <sep /> 2 </cn> </apply> </apply> </apply> <apply> <sum /> <bvar> <ci> k </ci> </bvar> <lowlimit> <cn type='integer'> 0 </cn> </lowlimit> <uplimit> <apply> <plus /> <apply> <times /> <cn type='integer'> 2 </cn> <ci> n </ci> </apply> <cn type='integer'> 1 </cn> </apply> </uplimit> <apply> <times /> <apply> <power /> <apply> <times /> <apply> <plus /> <apply> <times /> 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Rule Form





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





2002-12-18