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CosIntegral






Mathematica Notation

Traditional Notation









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





http://functions.wolfram.com/06.38.21.0068.01









  


  










Input Form





Integrate[z SinIntegral[b z] CosIntegral[a z], z] == (1/(8 a^2 b^2)) ((2 a^2 E^(I (a + b) z) CosIntegral[a z] (I (Gamma[2, (-I) b z] - Gamma[2, I b z]) + 2 b^2 z^2 SinIntegral[b z]) - I ((-a) b (-1 + E^(2 I a z)) (1 + E^(2 I b z)) + (a^2 + b^2) E^(I (a + b) z) (ExpIntegralEi[(-I) (a - b) z] - ExpIntegralEi[I (a - b) z] - ExpIntegralEi[(-I) (a + b) z] + ExpIntegralEi[I (a + b) z]) - 2 I b^2 E^(I (a + b) z) (Gamma[2, (-I) a z] + Gamma[2, I a z]) SinIntegral[b z]))/ E^(I (a + b) z))










Standard Form





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MathML Form







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





2001-10-29