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Sin






Mathematica Notation

Traditional Notation









Elementary Functions > Sin[z] > Integration > Indefinite integration > Involving functions of the direct function and exponential function > Involving products of the direct function and exponential function > Involving products of two direct functions and exponential function > Involving ep zrsin(b zr)sin(c z)





http://functions.wolfram.com/01.06.21.1355.01









  


  










Input Form





Integrate[E^(p Sqrt[z]) Sin[b Sqrt[z]] Sin[c z], z] == (1/(8 c^(3/2))) (-2 I Sqrt[c] E^(((-I) b + p) Sqrt[z] - I c z) + 2 I Sqrt[c] E^((I b + p) Sqrt[z] - I c z) - 2 I Sqrt[c] E^(((-I) b + p) Sqrt[z] + I c z) + 2 I Sqrt[c] E^((I b + p) Sqrt[z] + I c z) + ((-1)^(3/4) b Sqrt[Pi] Erfi[((-1)^(1/4) (b + I p - 2 c Sqrt[z]))/ (2 Sqrt[c])])/E^((I (b + I p)^2)/(4 c)) + (-1)^(3/4) E^((I (b + I p)^2)/(4 c)) p Sqrt[Pi] Erfi[((-1)^(1/4) ((-I) b + p - 2 I c Sqrt[z]))/(2 Sqrt[c])] - (-1)^(3/4) E^((I (b - I p)^2)/(4 c)) p Sqrt[Pi] Erfi[((-1)^(1/4) (I b + p - 2 I c Sqrt[z]))/(2 Sqrt[c])] - ((-1)^(1/4) p Sqrt[Pi] Erfi[((-1)^(3/4) ((-I) b + p + 2 I c Sqrt[z]))/ (2 Sqrt[c])])/E^((I (b + I p)^2)/(4 c)) + ((-1)^(1/4) p Sqrt[Pi] Erfi[((-1)^(3/4) (I b + p + 2 I c Sqrt[z]))/ (2 Sqrt[c])])/E^((I (b - I p)^2)/(4 c)) - ((-1)^(3/4) b Sqrt[Pi] Erfi[((-1)^(1/4) (b - I p + 2 c Sqrt[z]))/ (2 Sqrt[c])])/E^((I (b - I p)^2)/(4 c)) - (-1)^(1/4) b E^((I (b - I p)^2)/(4 c)) Sqrt[Pi] Erfi[((-1)^(3/4) (-b + I p + 2 c Sqrt[z]))/(2 Sqrt[c])] - (-1)^(1/4) b E^((I (b + I p)^2)/(4 c)) Sqrt[Pi] Erfi[((-1)^(3/4) (b + I p + 2 c Sqrt[z]))/(2 Sqrt[c])])










Standard Form





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MathML Form







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</apply> </apply> </apply> <cn type='integer'> 2 </cn> </apply> <apply> <power /> <apply> <times /> <cn type='integer'> 4 </cn> <ci> c </ci> </apply> <cn type='integer'> -1 </cn> </apply> </apply> </apply> </apply> <apply> <power /> <pi /> <cn type='rational'> 1 <sep /> 2 </cn> </apply> <apply> <ci> Erfi </ci> <apply> <times /> <apply> <power /> <cn type='integer'> -1 </cn> <cn type='rational'> 1 <sep /> 4 </cn> </apply> <apply> <plus /> <ci> b </ci> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <imaginaryi /> <ci> p </ci> </apply> </apply> <apply> <times /> <cn type='integer'> 2 </cn> <ci> c </ci> <apply> <power /> <ci> z </ci> <cn type='rational'> 1 <sep /> 2 </cn> </apply> </apply> </apply> <apply> <power /> <apply> <times /> <cn type='integer'> 2 </cn> <apply> <power /> <ci> c </ci> <cn type='rational'> 1 <sep /> 2 </cn> </apply> </apply> <cn type='integer'> -1 </cn> </apply> </apply> </apply> </apply> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <apply> <power /> <cn type='integer'> -1 </cn> <cn type='rational'> 1 <sep /> 4 </cn> </apply> <ci> b </ci> <apply> <power /> <exponentiale /> <apply> <times /> <imaginaryi /> <apply> <power /> <apply> <plus /> <ci> b </ci> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <imaginaryi /> <ci> p </ci> </apply> </apply> </apply> <cn type='integer'> 2 </cn> </apply> <apply> <power /> <apply> <times /> <cn type='integer'> 4 </cn> <ci> c </ci> </apply> <cn type='integer'> -1 </cn> </apply> </apply> </apply> <apply> <power /> <pi /> <cn type='rational'> 1 <sep /> 2 </cn> </apply> <apply> <ci> Erfi </ci> <apply> <times /> <apply> <power /> <cn type='integer'> -1 </cn> <cn type='rational'> 3 <sep /> 4 </cn> </apply> <apply> <plus /> <apply> <times /> <cn type='integer'> -1 </cn> <ci> b </ci> </apply> <apply> <times /> <imaginaryi /> <ci> p </ci> </apply> <apply> <times /> <cn type='integer'> 2 </cn> <ci> c </ci> <apply> <power /> <ci> z </ci> <cn type='rational'> 1 <sep /> 2 </cn> </apply> </apply> </apply> <apply> <power /> <apply> <times /> <cn type='integer'> 2 </cn> <apply> <power /> <ci> c </ci> <cn type='rational'> 1 <sep /> 2 </cn> </apply> </apply> <cn type='integer'> -1 </cn> </apply> </apply> </apply> </apply> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <apply> <power /> <cn type='integer'> -1 </cn> <cn type='rational'> 1 <sep /> 4 </cn> </apply> <ci> b </ci> <apply> <power /> <exponentiale /> <apply> <times /> <imaginaryi /> <apply> <power /> <apply> <plus /> <ci> b </ci> <apply> <times /> <imaginaryi /> <ci> p </ci> </apply> </apply> <cn type='integer'> 2 </cn> </apply> <apply> <power /> <apply> <times /> <cn type='integer'> 4 </cn> <ci> c </ci> </apply> <cn type='integer'> -1 </cn> </apply> </apply> </apply> <apply> <power /> <pi /> <cn type='rational'> 1 <sep /> 2 </cn> </apply> <apply> <ci> Erfi </ci> <apply> <times /> <apply> <power /> <cn type='integer'> -1 </cn> <cn type='rational'> 3 <sep /> 4 </cn> </apply> <apply> <plus /> <ci> b </ci> <apply> <times /> <imaginaryi /> <ci> p </ci> </apply> <apply> <times /> <cn type='integer'> 2 </cn> <ci> c </ci> <apply> <power /> <ci> z </ci> <cn type='rational'> 1 <sep /> 2 </cn> </apply> </apply> </apply> <apply> <power /> <apply> <times /> <cn type='integer'> 2 </cn> <apply> <power /> <ci> c </ci> <cn type='rational'> 1 <sep /> 2 </cn> </apply> </apply> <cn type='integer'> -1 </cn> </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