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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-1 eb z+e sin(c z)





http://functions.wolfram.com/01.06.21.0344.01









  


  










Input Form





Integrate[z^(7/2) E^(b z + e) Sin[c z], z] == (-(1/2)) I z^(9/2) E^e ((E^((b - I c) z) ((-(b - I c)) z)^(7/2) + ((7/16) (15 E^(I c z) Sqrt[Pi] + 2 E^(b z) Sqrt[(-(b - I c)) z] (15 + 10 I c z + 4 b^2 z^2 - 4 c^2 z^2 + 2 b z (-5 - 4 I c z)) - 15 E^(I c z) Sqrt[Pi] Erf[Sqrt[(-(b - I c)) z]]))/E^(I c z))/ ((-(b - I c)) z)^(9/2) - (E^((b + I c) z) ((-(b + I c)) z)^(7/2) + (7/16) (15 Sqrt[Pi] + 2 E^((b + I c) z) Sqrt[(-(b + I c)) z] (15 - 10 I c z + 4 b^2 z^2 - 4 c^2 z^2 + 2 b z (-5 + 4 I c z)) - 15 Sqrt[Pi] Erf[Sqrt[(-(b + I c)) z]]))/((-(b + I c)) z)^(9/2))










Standard Form





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MathML Form







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</apply> </apply> </apply> </apply> </apply> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <apply> <times /> <cn type='integer'> 1 </cn> <apply> <power /> <apply> <power /> <apply> <times /> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <plus /> <ci> b </ci> <apply> <times /> <imaginaryi /> <ci> c </ci> </apply> </apply> </apply> <ci> z </ci> </apply> <cn type='rational'> 9 <sep /> 2 </cn> </apply> <cn type='integer'> -1 </cn> </apply> </apply> <apply> <plus /> <apply> <times /> <apply> <power /> <exponentiale /> <apply> <times /> <apply> <plus /> <ci> b </ci> <apply> <times /> <imaginaryi /> <ci> c </ci> </apply> </apply> <ci> z </ci> </apply> </apply> <apply> <power /> <apply> <times /> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <plus /> <ci> b </ci> <apply> <times /> <imaginaryi /> <ci> c </ci> </apply> </apply> </apply> <ci> z </ci> </apply> <cn type='rational'> 7 <sep /> 2 </cn> </apply> </apply> <apply> <times /> <cn type='rational'> 7 <sep /> 16 </cn> <apply> <plus /> <apply> <times /> <cn type='integer'> 2 </cn> <apply> <power /> <exponentiale /> <apply> <times /> <apply> <plus /> <ci> b </ci> <apply> <times /> <imaginaryi /> <ci> c </ci> </apply> </apply> <ci> z </ci> </apply> </apply> <apply> <power /> <apply> <times /> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <plus /> <ci> b </ci> <apply> <times /> <imaginaryi /> <ci> c </ci> </apply> </apply> </apply> <ci> z </ci> </apply> <cn type='rational'> 1 <sep /> 2 </cn> </apply> <apply> <plus /> <apply> <times /> <cn type='integer'> 4 </cn> <apply> <power /> <ci> b </ci> <cn type='integer'> 2 </cn> </apply> <apply> <power /> <ci> z </ci> <cn type='integer'> 2 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <cn type='integer'> 4 </cn> <apply> <power /> <ci> c </ci> <cn type='integer'> 2 </cn> </apply> <apply> <power /> <ci> z </ci> <cn type='integer'> 2 </cn> </apply> </apply> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <cn type='integer'> 10 </cn> <imaginaryi /> <ci> c </ci> <ci> z </ci> </apply> </apply> <apply> <times /> <cn type='integer'> 2 </cn> <ci> b </ci> <apply> <plus /> <apply> <times /> <cn type='integer'> 4 </cn> <imaginaryi /> <ci> c </ci> <ci> z </ci> </apply> <cn type='integer'> -5 </cn> </apply> <ci> z </ci> </apply> <cn type='integer'> 15 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <cn type='integer'> 15 </cn> <apply> <power /> <pi /> <cn type='rational'> 1 <sep /> 2 </cn> </apply> <apply> <ci> Erf </ci> <apply> <power /> <apply> <times /> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <plus /> <ci> b </ci> <apply> <times /> <imaginaryi /> <ci> c </ci> </apply> </apply> </apply> <ci> z </ci> </apply> <cn type='rational'> 1 <sep /> 2 </cn> </apply> </apply> </apply> </apply> <apply> <times /> <cn type='integer'> 15 </cn> <apply> <power /> <pi /> <cn type='rational'> 1 <sep /> 2 </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