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SinIntegral






Mathematica Notation

Traditional Notation









Gamma, Beta, Erf > SinIntegral[z] > Integration > Indefinite integration > Involving functions of the direct function and elementary functions > Involving elementary functions of the direct function and elementary functions > Involving products of the direct function and a power function





http://functions.wolfram.com/06.37.21.0059.01









  


  










Input Form





Integrate[z^3 SinIntegral[a z] SinIntegral[b z], z] == (1/8) (-((2 (3 (a^2 - b^2)^2 (a^4 + b^4) CosIntegral[(a - b) z] - 3 (a^2 - b^2)^2 (a^4 + b^4) CosIntegral[(a + b) z] - a b (a b Sin[a z] (b (a^4 + 2 a^2 b^2 - 3 b^4) z Cos[b z] + (-3 a^4 + 14 a^2 b^2 - 3 b^4) Sin[b z]) + Cos[a z] ((-6 b^6 + a^6 (-6 + b^2 z^2) - 2 a^4 b^2 (-5 + b^2 z^2) + a^2 b^4 (10 + b^2 z^2)) Cos[b z] + a^2 b (-3 a^4 + 2 a^2 b^2 + b^4) z Sin[b z]))))/(a^4 (a - b)^2 b^4 (a + b)^2)) + (1/b^4) (2 (b z (-6 + b^2 z^2) Cos[b z] - 3 (-2 + b^2 z^2) Sin[b z]) SinIntegral[a z]) + (1/a^4) (2 (a z (-6 + a^2 z^2) Cos[a z] - 3 (-2 + a^2 z^2) Sin[a z] + a^4 z^4 SinIntegral[a z]) SinIntegral[b z]))










Standard Form





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MathML Form







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<msup> <mi> b </mi> <mn> 4 </mn> </msup> </mrow> <mo> ) </mo> </mrow> <mo> &#8290; </mo> <mi> z </mi> <mo> &#8290; </mo> <mrow> <mi> sin </mi> <mo> &#8289; </mo> <mo> ( </mo> <mrow> <mi> b </mi> <mo> &#8290; </mo> <mi> z </mi> </mrow> <mo> ) </mo> </mrow> <mo> &#8290; </mo> <msup> <mi> a </mi> <mn> 2 </mn> </msup> </mrow> <mo> + </mo> <mrow> <mrow> <mo> ( </mo> <mrow> <mrow> <mrow> <mo> ( </mo> <mrow> <mrow> <msup> <mi> b </mi> <mn> 2 </mn> </msup> <mo> &#8290; </mo> <msup> <mi> z </mi> <mn> 2 </mn> </msup> </mrow> <mo> - </mo> <mn> 6 </mn> </mrow> <mo> ) </mo> </mrow> <mo> &#8290; </mo> <msup> <mi> a </mi> <mn> 6 </mn> </msup> </mrow> <mo> - </mo> <mrow> <mn> 2 </mn> <mo> &#8290; </mo> <msup> <mi> b </mi> <mn> 2 </mn> </msup> <mo> &#8290; </mo> <mrow> <mo> ( </mo> <mrow> <mrow> <msup> <mi> b </mi> <mn> 2 </mn> </msup> <mo> &#8290; </mo> <msup> <mi> z </mi> <mn> 2 </mn> </msup> </mrow> <mo> - </mo> <mn> 5 </mn> </mrow> <mo> ) </mo> </mrow> <mo> &#8290; </mo> <msup> <mi> a </mi> <mn> 4 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</semantics> </math>










Rule Form





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





2001-10-29





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