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ExpIntegralEi






Mathematica Notation

Traditional Notation









Gamma, Beta, Erf > ExpIntegralEi[z] > Integration > Indefinite integration > Involving one direct function and elementary functions > Involving trigonometric functions and a power function > Involving cos and power





http://functions.wolfram.com/06.35.21.0036.01









  


  










Input Form





Integrate[z^3 Cos[b z] ExpIntegralEi[a z], z] == (1/b^4) ((1/(a^2 + b^2)^3) (b^2 E^(a z) (-3 a^4 - 6 a^2 b^2 - 11 b^4 - a (a^2 + b^2) (3 a^2 + 7 b^2) z + b^2 (a^2 + b^2)^2 z^2) Cos[b z]) + 3 (ExpIntegralEi[(a - I b) z] + ExpIntegralEi[(a + I b) z]) - (1/(a^2 + b^2)^3) (b E^(a z) (-2 a (3 a^4 + 8 a^2 b^2 + 9 b^4) + b^2 (a^2 + b^2) (a^2 + 5 b^2) z + a b^2 (a^2 + b^2)^2 z^2) Sin[b z]) + ExpIntegralEi[a z] (3 (-2 + b^2 z^2) Cos[b z] + b z (-6 + b^2 z^2) Sin[b z]))










Standard Form





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MathML Form







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/> <apply> <times /> <apply> <power /> <ci> b </ci> <cn type='integer'> 2 </cn> </apply> <apply> <power /> <ci> z </ci> <cn type='integer'> 2 </cn> </apply> </apply> <cn type='integer'> -2 </cn> </apply> <apply> <cos /> <apply> <times /> <ci> b </ci> <ci> z </ci> </apply> </apply> </apply> <apply> <times /> <ci> b </ci> <ci> z </ci> <apply> <plus /> <apply> <times /> <apply> <power /> <ci> b </ci> <cn type='integer'> 2 </cn> </apply> <apply> <power /> <ci> z </ci> <cn type='integer'> 2 </cn> </apply> </apply> <cn type='integer'> -6 </cn> </apply> <apply> <sin /> <apply> <times /> <ci> b </ci> <ci> z </ci> </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