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SinhIntegral






Mathematica Notation

Traditional Notation









Gamma, Beta, Erf > SinhIntegral[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/06.39.21.0056.01









  


  










Input Form





Integrate[z^2 SinhIntegral[a z] SinhIntegral[b z], z] == (1/6) (-((1/b^3) (2 ((2 + b^2 z^2) Cosh[b z] - 2 b z Sinh[b z]) SinhIntegral[a z])) + (1/a^3) (2 ((-(2 + a^2 z^2)) Cosh[a z] + 2 a z Sinh[a z] + a^3 z^3 SinhIntegral[a z]) SinhIntegral[b z]) + (2 (a b (b (a^2 + 2 b^2) Cosh[b z] Sinh[a z] + a Cosh[a z] (b (a^2 - b^2) z Cosh[b z] - (2 a^2 + b^2) Sinh[b z])) + (a^5 - a^3 b^2 - a^2 b^3 + b^5) SinhIntegral[(a - b) z] + (a^5 - a^3 b^2 + a^2 b^3 - b^5) SinhIntegral[(a + b) z]))/ (a^3 (a - b) b^3 (a + b)))










Standard Form





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MathML Form







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</cn> </apply> </apply> <cn type='integer'> 2 </cn> </apply> <apply> <cosh /> <apply> <times /> <ci> a </ci> <ci> z </ci> </apply> </apply> </apply> </apply> </apply> <apply> <ci> SinhIntegral </ci> <apply> <times /> <ci> b </ci> <ci> z </ci> </apply> </apply> </apply> </apply> <apply> <times /> <apply> <times /> <cn type='integer'> 1 </cn> <apply> <power /> <apply> <times /> <apply> <power /> <ci> a </ci> <cn type='integer'> 3 </cn> </apply> <apply> <plus /> <ci> a </ci> <apply> <times /> <cn type='integer'> -1 </cn> <ci> b </ci> </apply> </apply> <apply> <power /> <ci> b </ci> <cn type='integer'> 3 </cn> </apply> <apply> <plus /> <ci> a </ci> <ci> b </ci> </apply> </apply> <cn type='integer'> -1 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> 2 </cn> <apply> <plus /> <apply> <times /> <ci> a </ci> <ci> b </ci> <apply> <plus /> <apply> <times /> <ci> b </ci> <apply> <plus /> <apply> <power /> <ci> a </ci> <cn type='integer'> 2 </cn> </apply> <apply> <times /> <cn 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type='integer'> 2 </cn> </apply> </apply> <apply> <sinh /> <apply> <times /> <ci> b </ci> <ci> z </ci> </apply> </apply> </apply> </apply> </apply> </apply> </apply> </apply> <apply> <times /> <apply> <plus /> <apply> <power /> <ci> a </ci> <cn type='integer'> 5 </cn> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <apply> <power /> <ci> b </ci> <cn type='integer'> 2 </cn> </apply> <apply> <power /> <ci> a </ci> <cn type='integer'> 3 </cn> </apply> </apply> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <apply> <power /> <ci> b </ci> <cn type='integer'> 3 </cn> </apply> <apply> <power /> <ci> a </ci> <cn type='integer'> 2 </cn> </apply> </apply> </apply> <apply> <power /> <ci> b </ci> <cn type='integer'> 5 </cn> </apply> </apply> <apply> <ci> SinhIntegral </ci> <apply> <times /> <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 /> <apply> <plus /> <apply> <power /> <ci> a </ci> <cn type='integer'> 5 </cn> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <apply> <power /> <ci> b </ci> <cn type='integer'> 2 </cn> </apply> <apply> <power /> <ci> a </ci> <cn type='integer'> 3 </cn> </apply> </apply> </apply> <apply> <times /> <apply> <power /> <ci> b </ci> <cn type='integer'> 3 </cn> </apply> <apply> <power /> <ci> a </ci> <cn type='integer'> 2 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <power /> <ci> b </ci> <cn type='integer'> 5 </cn> </apply> </apply> </apply> <apply> <ci> SinhIntegral </ci> <apply> <times /> <apply> <plus /> <ci> a </ci> <ci> b </ci> </apply> <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