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SinIntegral




Mathematica Notation

Traditional Notation









Gamma, Beta, Erf > SinIntegral[z] > Integration > Indefinite integration > Involving direct function and Gamma-, Beta-, Erf-type functions > Involving exponential integral-type functions and a power function > Involving Ei and power





http://functions.wolfram.com/06.37.21.0063.01









  


  








Input Form





Integrate[z^2 ExpIntegralEi[b z] SinIntegral[a z], z] == (1/3) (-((1/b^3) (I (-ExpIntegralEi[((-I) a + b) z] + ExpIntegralEi[(I a + b) z] + (1/2) b ((2 I E^(((-I) a + b) z))/ (a + I b) - (2 E^((I a + b) z))/(I a + b) + (b Gamma[2, (-I) a z - b z])/(a - I b)^2 + (b Gamma[2, I a z - b z])/ ((-I) a + b)^2)))) - (1/(2 a^3)) ((2 a E^(((-I) a + b) z))/(a + I b) + (2 a E^((I a + b) z))/(a - I b) - 2 ExpIntegralEi[((-I) a + b) z] - 2 ExpIntegralEi[(I a + b) z] + (a^2 Gamma[2, (-I) a z - b z])/(a - I b)^2 + (a^2 Gamma[2, I a z - b z])/ (a + I b)^2 + ExpIntegralEi[b z] Gamma[3, (-I) a z] + ExpIntegralEi[b z] Gamma[3, I a z]) + (z^3 ExpIntegralEi[b z] - Gamma[3, (-b) z]/b^3) SinIntegral[a z])








Standard Form





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MathML Form







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type='integer'> -1 </cn> <apply> <times /> <ci> b </ci> <ci> z </ci> </apply> </apply> </apply> </apply> <apply> <power /> <apply> <power /> <apply> <plus /> <ci> b </ci> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <imaginaryi /> <ci> a </ci> </apply> </apply> </apply> <cn type='integer'> 2 </cn> </apply> <cn type='integer'> -1 </cn> </apply> </apply> </apply> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <ci> ExpIntegralEi </ci> <apply> <times /> <apply> <plus /> <ci> b </ci> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <imaginaryi /> <ci> a </ci> </apply> </apply> </apply> <ci> z </ci> </apply> </apply> </apply> <apply> <ci> ExpIntegralEi </ci> <apply> <times /> <apply> <plus /> <ci> b </ci> <apply> <times /> <ci> a </ci> <imaginaryi /> </apply> </apply> <ci> z </ci> </apply> </apply> </apply> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <apply> <times /> <cn type='integer'> 1 </cn> <apply> <power /> <apply> <times /> <cn type='integer'> 2 </cn> <apply> <power /> <ci> a </ci> <cn type='integer'> 3 </cn> </apply> </apply> <cn type='integer'> -1 </cn> </apply> </apply> <apply> <plus /> <apply> <times /> <apply> <ci> Gamma </ci> <cn type='integer'> 2 </cn> <apply> <plus /> <apply> <times /> <apply> <times /> <cn type='integer'> -1 </cn> <ci> b </ci> </apply> <ci> z </ci> </apply> <apply> <times /> <ci> a </ci> <apply> <times /> <cn type='integer'> -1 </cn> <imaginaryi /> </apply> <ci> z </ci> </apply> </apply> </apply> <apply> <power /> <ci> a </ci> <cn type='integer'> 2 </cn> </apply> <apply> <power /> <apply> <power /> <apply> <plus /> <ci> a </ci> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <imaginaryi /> <ci> b </ci> </apply> </apply> </apply> <cn type='integer'> 2 </cn> </apply> <cn type='integer'> -1 </cn> </apply> </apply> <apply> <times /> <apply> <ci> Gamma </ci> <cn type='integer'> 2 </cn> <apply> <plus /> <apply> <times /> <imaginaryi /> <ci> a </ci> <ci> z </ci> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <ci> b </ci> <ci> z </ci> </apply> </apply> </apply> </apply> <apply> <power /> <ci> a </ci> <cn type='integer'> 2 </cn> </apply> <apply> <power /> <apply> <power /> <apply> <plus /> <ci> a </ci> <apply> <times /> <ci> b </ci> <imaginaryi /> </apply> </apply> <cn type='integer'> 2 </cn> </apply> <cn type='integer'> -1 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> 2 </cn> <apply> <power /> <exponentiale /> <apply> <times /> <apply> <plus /> <ci> b </ci> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <imaginaryi /> <ci> a </ci> </apply> </apply> </apply> <ci> z </ci> </apply> </apply> <ci> a </ci> <apply> <power /> <apply> <plus /> <ci> a </ci> <apply> <times /> <ci> b </ci> <imaginaryi /> </apply> </apply> <cn type='integer'> -1 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> 2 </cn> <apply> <power /> <exponentiale /> <apply> <times /> <apply> <plus /> <ci> b </ci> <apply> <times /> <ci> a </ci> <imaginaryi /> </apply> </apply> <ci> z </ci> </apply> </apply> <ci> a </ci> <apply> <power /> <apply> <plus /> <ci> a </ci> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <imaginaryi /> <ci> b </ci> </apply> </apply> </apply> <cn type='integer'> -1 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <cn type='integer'> 2 </cn> <apply> <ci> ExpIntegralEi </ci> <apply> <times /> <apply> <plus /> <ci> b </ci> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <imaginaryi /> <ci> a </ci> </apply> </apply> </apply> <ci> z </ci> </apply> </apply> </apply> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <cn type='integer'> 2 </cn> <apply> <ci> ExpIntegralEi </ci> <apply> <times /> <apply> <plus /> <ci> b </ci> <apply> <times /> <ci> a </ci> <imaginaryi /> </apply> </apply> <ci> z </ci> </apply> </apply> </apply> </apply> <apply> <times /> <apply> <ci> ExpIntegralEi </ci> <apply> <times /> <ci> b </ci> <ci> z </ci> </apply> </apply> <apply> <ci> Gamma </ci> <cn type='integer'> 3 </cn> <apply> <times /> <apply> <times /> <cn type='integer'> -1 </cn> <imaginaryi /> </apply> <ci> a </ci> <ci> z </ci> </apply> </apply> </apply> <apply> <times /> <apply> <ci> ExpIntegralEi </ci> <apply> <times /> <ci> b </ci> <ci> z </ci> </apply> </apply> <apply> <ci> Gamma </ci> <cn type='integer'> 3 </cn> <apply> <times /> <imaginaryi /> <ci> a </ci> <ci> z </ci> </apply> </apply> </apply> </apply> </apply> </apply> <apply> <times /> <apply> <plus /> <apply> <times /> <apply> <power /> <ci> z </ci> <cn type='integer'> 3 </cn> </apply> <apply> <ci> ExpIntegralEi </ci> <apply> <times /> <ci> b </ci> <ci> z </ci> </apply> </apply> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <apply> <ci> Gamma </ci> <cn type='integer'> 3 </cn> <apply> <times /> <apply> <times /> <cn type='integer'> -1 </cn> <ci> b </ci> </apply> <ci> z </ci> 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Rule Form





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





2001-10-29