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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 cosh and power





http://functions.wolfram.com/06.39.21.0039.01









  


  










Input Form





Integrate[z^n Cosh[a z] SinhIntegral[a z], z] == (1/((-a)^n (4 a))) (2 (Gamma[1 + n, (-a) z] - (-1)^n Gamma[1 + n, a z]) SinhIntegral[a z] - n! ((-1)^n ExpIntegralEi[-2 a z] + ExpIntegralEi[2 a z] - (1 + (-1)^n) Log[z] - 2 Sum[(((-a) z)^k/(2 k) + 2^(-1 - k) Gamma[k, -2 a z])/k!, {k, 1, n}] - 2 (-1)^n Sum[((a z)^k/(2 k) + 2^(-1 - k) Gamma[k, 2 a z])/k!, {k, 1, n}])) /; Element[n, Integers] && n >= 0










Standard Form





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MathML Form







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<mn> 1 </mn> </mrow> <mi> n </mi> </munderover> <mrow> <mfrac> <mn> 1 </mn> <mrow> <mi> k </mi> <mo> ! </mo> </mrow> </mfrac> <mo> &#8290; </mo> <mrow> <mo> ( </mo> <mrow> <mfrac> <msup> <mrow> <mo> ( </mo> <mrow> <mi> a </mi> <mo> &#8290; </mo> <mi> z </mi> </mrow> <mo> ) </mo> </mrow> <mi> k </mi> </msup> <mrow> <mn> 2 </mn> <mo> &#8290; </mo> <mi> k </mi> </mrow> </mfrac> <mo> + </mo> <mrow> <msup> <mn> 2 </mn> <mrow> <mrow> <mo> - </mo> <mi> k </mi> </mrow> <mo> - </mo> <mn> 1 </mn> </mrow> </msup> <mo> &#8290; </mo> <mrow> <mi> &#915; </mi> <mo> &#8289; </mo> <mo> ( </mo> <mrow> <mi> k </mi> <mo> , </mo> <mrow> <mn> 2 </mn> <mo> &#8290; </mo> <mi> a </mi> <mo> &#8290; </mo> <mi> z </mi> </mrow> </mrow> <mo> ) </mo> </mrow> </mrow> </mrow> <mo> ) </mo> </mrow> </mrow> </mrow> </mrow> </mrow> <mo> ) </mo> </mrow> </mrow> </mrow> <mo> ) </mo> </mrow> </mrow> </mrow> <mo> /; </mo> <mrow> <mi> n </mi> <mo> &#8712; </mo> <mi> &#8469; </mi> </mrow> </mrow> <annotation-xml 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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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