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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/01.06.21.0469.01









  


  










Input Form





Integrate[z^4 E^(b z^2 + e) Sin[c z^2 + g], z] == (1/16) z^5 E^e ((-I) Cos[g] ((3 Sqrt[Pi] - 2 E^((b - I c) z^2) Sqrt[(-(b - I c)) z^2] (-3 + 2 b z^2 - 2 I c z^2) - 3 Sqrt[Pi] Erf[Sqrt[(-(b - I c)) z^2]])/ ((-(b - I c)) z^2)^(5/2) + (-3 Sqrt[Pi] + 2 E^((b + I c) z^2) Sqrt[(-(b + I c)) z^2] (-3 + 2 b z^2 + 2 I c z^2) + 3 Sqrt[Pi] Erf[Sqrt[(-(b + I c)) z^2]])/((-(b + I c)) z^2)^(5/2)) + ((-3 Sqrt[Pi] + 2 E^((b - I c) z^2) Sqrt[(-(b - I c)) z^2] (-3 + 2 b z^2 - 2 I c z^2) + 3 Sqrt[Pi] Erf[Sqrt[(-(b - I c)) z^2]])/ ((-(b - I c)) z^2)^(5/2) + (-3 Sqrt[Pi] + 2 E^((b + I c) z^2) Sqrt[(-(b + I c)) z^2] (-3 + 2 b z^2 + 2 I c z^2) + 3 Sqrt[Pi] Erf[Sqrt[(-(b + I c)) z^2]])/((-(b + I c)) z^2)^(5/2)) Sin[g])










Standard Form





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MathML Form







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2 </cn> </apply> </apply> <ci> e </ci> </apply> </apply> <apply> <sin /> <apply> <plus /> <apply> <times /> <ci> c </ci> <apply> <power /> <ci> z </ci> <cn type='integer'> 2 </cn> </apply> </apply> <ci> g </ci> </apply> </apply> </apply> </apply> <apply> <times /> <cn type='rational'> 1 <sep /> 16 </cn> <apply> <power /> <ci> z </ci> <cn type='integer'> 5 </cn> </apply> <apply> <power /> <exponentiale /> <ci> e </ci> </apply> <apply> <plus /> <apply> <times /> <apply> <plus /> <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> <apply> <power /> <ci> z </ci> <cn type='integer'> 2 </cn> </apply> </apply> <cn type='rational'> 5 <sep /> 2 </cn> </apply> <cn type='integer'> -1 </cn> </apply> </apply> <apply> <plus /> <apply> <times /> <cn type='integer'> 2 </cn> <apply> <power 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type='integer'> -1 </cn> <apply> <times /> <imaginaryi /> <apply> <cos /> <ci> g </ci> </apply> <apply> <plus /> <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> <apply> <power /> <ci> z </ci> <cn type='integer'> 2 </cn> </apply> </apply> <cn type='rational'> 5 <sep /> 2 </cn> </apply> <cn type='integer'> -1 </cn> </apply> </apply> <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> <apply> <power /> <ci> z </ci> <cn type='integer'> 2 </cn> </apply> </apply> </apply> <apply> <power /> <apply> <times /> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <plus /> <ci> b </ci> <apply> <times /> <imaginaryi /> <ci> 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Rule Form





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





2002-12-18