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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 hyperbolic functions and a power function > Involving cosh and power





http://functions.wolfram.com/06.35.21.0050.01









  


  










Input Form





Integrate[z^3 Cosh[b z] ExpIntegralEi[a z], z] == (1/b^4) (ExpIntegralEi[a z] (-3 (2 + b^2 z^2) Cosh[b z] + b z (6 + b^2 z^2) Sinh[b z]) + (1/((a - b)^3 (a + b)^3)) (b^2 E^(a z) (3 a^4 - 6 a^2 b^2 + 11 b^4 + a (3 a^4 - 10 a^2 b^2 + 7 b^4) z + b^2 (a^2 - b^2)^2 z^2) Cosh[b z] + 3 (a^2 - b^2)^3 (ExpIntegralEi[(a - b) z] + ExpIntegralEi[(a + b) z]) - b E^(a z) (2 a (3 a^4 - 8 a^2 b^2 + 9 b^4) + b^2 (a^4 - 6 a^2 b^2 + 5 b^4) z + a b^2 (a^2 - b^2)^2 z^2) Sinh[b z]))










Standard Form





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MathML Form







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type='integer'> 2 </cn> <ci> a </ci> <apply> <plus /> <apply> <times /> <cn type='integer'> 3 </cn> <apply> <power /> <ci> a </ci> <cn type='integer'> 4 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <cn type='integer'> 8 </cn> <apply> <power /> <ci> b </ci> <cn type='integer'> 2 </cn> </apply> <apply> <power /> <ci> a </ci> <cn type='integer'> 2 </cn> </apply> </apply> </apply> <apply> <times /> <cn type='integer'> 9 </cn> <apply> <power /> <ci> b </ci> <cn type='integer'> 4 </cn> </apply> </apply> </apply> </apply> </apply> <apply> <sinh /> <apply> <times /> <ci> b </ci> <ci> z </ci> </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