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SinhIntegral






Mathematica Notation

Traditional Notation









Gamma, Beta, Erf > SinhIntegral[z] > Integration > Indefinite integration > Involving one direct function and elementary functions > Involving hyperbolic functions and a power function > Involving sinh and power





http://functions.wolfram.com/06.39.21.0036.01









  


  










Input Form





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










Standard Form





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MathML Form







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