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Sin






Mathematica Notation

Traditional Notation









Elementary Functions > Sin[z] > Integration > Indefinite integration > Involving one direct function and elementary functions > Involving rational functions > Involving (a z2+b)-n





http://functions.wolfram.com/01.06.21.0155.01









  


  










Input Form





Integrate[Sin[c z]/(a z^2 + b)^2, z] == ((-(b + a z^2)) CosIntegral[c (-((I Sqrt[b])/Sqrt[a]) + z)] (Sqrt[b] c Cosh[(Sqrt[b] c)/Sqrt[a]] - Sqrt[a] Sinh[(Sqrt[b] c)/Sqrt[a]]) - (b + a z^2) CosIntegral[c ((I Sqrt[b])/Sqrt[a] + z)] (Sqrt[b] c Cosh[(Sqrt[b] c)/Sqrt[a]] - Sqrt[a] Sinh[(Sqrt[b] c)/Sqrt[a]]) - I (Sqrt[a] (b + a z^2) Cosh[(Sqrt[b] c)/Sqrt[a]] SinIntegral[c (-((I Sqrt[b])/Sqrt[a]) + z)] + (b + a z^2) ((-Sqrt[a]) Cosh[(Sqrt[b] c)/Sqrt[a]] + Sqrt[b] c Sinh[(Sqrt[b] c)/Sqrt[a]]) SinIntegral[ c ((I Sqrt[b])/Sqrt[a] + z)] + Sqrt[b] (2 I a z Sin[c z] + c (b + a z^2) Sinh[(Sqrt[b] c)/Sqrt[a]] SinIntegral[ (I Sqrt[b] c)/Sqrt[a] - c z])))/(4 a b^(3/2) (b + a z^2))










Standard Form





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MathML Form







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/> <ci> a </ci> <apply> <power /> <ci> z </ci> <cn type='integer'> 2 </cn> </apply> </apply> <ci> b </ci> </apply> <apply> <plus /> <apply> <times /> <apply> <power /> <ci> b </ci> <cn type='rational'> 1 <sep /> 2 </cn> </apply> <ci> c </ci> <apply> <sinh /> <apply> <times /> <apply> <power /> <ci> b </ci> <cn type='rational'> 1 <sep /> 2 </cn> </apply> <ci> c </ci> <apply> <power /> <apply> <power /> <ci> a </ci> <cn type='rational'> 1 <sep /> 2 </cn> </apply> <cn type='integer'> -1 </cn> </apply> </apply> </apply> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <apply> <power /> <ci> a </ci> <cn type='rational'> 1 <sep /> 2 </cn> </apply> <apply> <cosh /> <apply> <times /> <apply> <power /> <ci> b </ci> <cn type='rational'> 1 <sep /> 2 </cn> </apply> <ci> c </ci> <apply> <power /> <apply> <power /> <ci> a </ci> <cn type='rational'> 1 <sep /> 2 </cn> </apply> <cn type='integer'> -1 </cn> </apply> </apply> </apply> </apply> </apply> </apply> <apply> <ci> SinIntegral </ci> <apply> <times /> <ci> c </ci> <apply> <plus /> <apply> <times /> <imaginaryi /> <apply> <power /> <ci> b </ci> <cn type='rational'> 1 <sep /> 2 </cn> </apply> <apply> <power /> <apply> <power /> <ci> a </ci> <cn type='rational'> 1 <sep /> 2 </cn> </apply> <cn type='integer'> -1 </cn> </apply> </apply> <ci> z </ci> </apply> </apply> </apply> </apply> <apply> <times /> <apply> <power /> <ci> a </ci> <cn type='rational'> 1 <sep /> 2 </cn> </apply> <apply> <plus /> <apply> <times /> <ci> a </ci> <apply> <power /> <ci> z </ci> <cn type='integer'> 2 </cn> </apply> </apply> <ci> b </ci> </apply> <apply> <cosh /> <apply> <times /> <apply> <power /> <ci> b </ci> <cn type='rational'> 1 <sep /> 2 </cn> </apply> <ci> c </ci> <apply> <power /> <apply> <power /> <ci> a </ci> <cn type='rational'> 1 <sep /> 2 </cn> </apply> <cn type='integer'> -1 </cn> </apply> </apply> </apply> <apply> <ci> SinIntegral </ci> <apply> <times /> <ci> c </ci> <apply> <plus /> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <imaginaryi /> <apply> <power /> <ci> b </ci> <cn type='rational'> 1 <sep /> 2 </cn> </apply> <apply> <power /> <apply> <power /> <ci> a </ci> <cn type='rational'> 1 <sep /> 2 </cn> </apply> <cn type='integer'> -1 </cn> </apply> </apply> </apply> <ci> z </ci> </apply> </apply> </apply> </apply> <apply> <times /> <apply> <power /> <ci> b </ci> <cn type='rational'> 1 <sep /> 2 </cn> </apply> <apply> <plus /> <apply> <times /> <cn type='integer'> 2 </cn> <ci> a </ci> <imaginaryi /> <ci> z </ci> <apply> <sin /> <apply> <times /> <ci> c </ci> <ci> z </ci> </apply> </apply> </apply> <apply> <times /> <ci> c </ci> <apply> <plus /> <apply> <times /> <ci> a </ci> <apply> <power /> <ci> z </ci> <cn type='integer'> 2 </cn> </apply> </apply> <ci> b </ci> </apply> <apply> <sinh /> <apply> <times /> <apply> <power /> <ci> b </ci> <cn type='rational'> 1 <sep /> 2 </cn> </apply> <ci> c </ci> <apply> <power /> <apply> <power /> <ci> a </ci> <cn type='rational'> 1 <sep /> 2 </cn> </apply> <cn type='integer'> -1 </cn> </apply> </apply> </apply> <apply> <ci> SinIntegral </ci> <apply> <plus /> <apply> <times /> <imaginaryi /> <apply> <power /> <ci> b </ci> <cn type='rational'> 1 <sep /> 2 </cn> </apply> <ci> c </ci> <apply> <power /> <apply> <power /> <ci> a </ci> <cn type='rational'> 1 <sep /> 2 </cn> </apply> <cn type='integer'> -1 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <ci> c </ci> <ci> z </ci> </apply> </apply> </apply> </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