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CoshIntegral






Mathematica Notation

Traditional Notation









Gamma, Beta, Erf > CoshIntegral[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/06.40.21.0057.01









  


  










Input Form





Integrate[z^3 CoshIntegral[a z] CoshIntegral[b z], z] == (a^2 b^2 Cosh[b z] ((-3 a^4 + 14 a^2 b^2 - 3 b^4) Cosh[a z] + a (-3 a^4 + 2 a^2 b^2 + b^4) z Sinh[a z]) + (a - b)^2 (a + b)^2 (3 b^4 (2 + a^2 z^2) Cosh[a z] CoshIntegral[b z] - 3 (a^4 + b^4) (CoshIntegral[(a - b) z] + CoshIntegral[(a + b) z]) - a b^4 z (6 + a^2 z^2) CoshIntegral[b z] Sinh[a z]) + a b (b^2 (a^5 + 2 a^3 b^2 - 3 a b^4) z Cosh[a z] + (2 (a^2 + b^2) (3 a^4 - 8 a^2 b^2 + 3 b^4) + a^2 b^2 (a^2 - b^2)^2 z^2) Sinh[a z]) Sinh[b z] + a^4 (a - b)^2 (a + b)^2 CoshIntegral[a z] (3 (2 + b^2 z^2) Cosh[b z] + b^4 z^4 CoshIntegral[b z] - b z (6 + b^2 z^2) Sinh[b z]))/(4 a^4 (a - b)^2 b^4 (a + b)^2)










Standard Form





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MathML Form







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type='integer'> 4 </cn> </apply> </apply> <apply> <times /> <apply> <power /> <ci> b </ci> <cn type='integer'> 2 </cn> </apply> <apply> <cosh /> <apply> <times /> <ci> b </ci> <ci> z </ci> </apply> </apply> <apply> <plus /> <apply> <times /> <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'> 14 </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> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <cn type='integer'> 3 </cn> <apply> <power /> <ci> b </ci> <cn type='integer'> 4 </cn> </apply> </apply> </apply> </apply> <apply> <cosh /> <apply> <times /> <ci> a </ci> <ci> z </ci> </apply> </apply> </apply> <apply> <times /> <ci> a </ci> <apply> <plus /> <apply> <times /> <cn type='integer'> -3 </cn> <apply> <power /> <ci> a </ci> <cn type='integer'> 4 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Rule Form





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





2001-10-29





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