Integrate[z^n Cosh[b z] CoshIntegral[a z], z] == ((b^(-1 - n) n!)/4) ((-(-1)^n) ExpIntegralEi[(-a + b) z] - (-1)^n ExpIntegralEi[(a + b) z] + ExpIntegralEi[(-a - b) z] + ExpIntegralEi[(a - b) z] + (-1)^n E^((-a + b) z) Sum[(1/m) (b/(b - a))^m (((-1)^k (b - a)^k z^k)/k!), {k, 0, n}, {m, k + 1, n}] - E^((a - b) z) Sum[(1/m) (b/(b - a))^m (((b - a)^k z^k)/k!), {k, 0, n}, {m, k + 1, n}] + (-1)^n E^((a + b) z) Sum[(1/m) (b/(b + a))^m (((-1)^k (a + b)^k z^k)/k!), {k, 0, n}, {m, k + 1, n}] - E^((-a - b) z) Sum[(1/m) (b/(b + a))^m (((a + b)^k z^k)/k!), {k, 0, n}, {m, k + 1, n}] + 4 Sinh[b z] CoshIntegral[a z] Sum[(b z)^(2 k + n - 2 Floor[n/2])/(2 k + n - 2 Floor[n/2])!, {k, 0, Floor[n/2]}] - 4 Cosh[b z] CoshIntegral[a z] Sum[(b z)^(2 k + n - 2 Floor[(n - 1)/2] - 1)/ (2 k + n - 2 Floor[(n - 1)/2] - 1)!, {k, 0, Floor[(n - 1)/2]}]) /; Element[n, Integers] && n >= 0

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b </mi> <mo> - </mo> <mi> a </mi> </mrow> <mo> ) </mo> </mrow> <mi> k </mi> </msup> <mo> &#8290; </mo> <msup> <mi> z </mi> <mi> k </mi> </msup> </mrow> <mo> ) </mo> </mrow> </mrow> <mrow> <mi> m </mi> <mo> &#8290; </mo> <mrow> <mi> k </mi> <mo> ! </mo> </mrow> </mrow> </mfrac> </mrow> </mrow> </mrow> <mo> - </mo> <mrow> <msup> <mi> &#8519; </mi> <mrow> <mrow> <mo> ( </mo> <mrow> <mrow> <mo> - </mo> <mi> a </mi> </mrow> <mo> - </mo> <mi> b </mi> </mrow> <mo> ) </mo> </mrow> <mo> &#8290; </mo> <mi> z </mi> </mrow> </msup> <mo> &#8290; </mo> <mrow> <munderover> <mo> &#8721; </mo> <mrow> <mi> k </mi> <mo> = </mo> <mn> 0 </mn> </mrow> <mi> n </mi> </munderover> <mrow> <munderover> <mo> &#8721; </mo> <mrow> <mi> m </mi> <mo> = </mo> <mrow> <mi> k </mi> <mo> + </mo> <mn> 1 </mn> </mrow> </mrow> <mi> n </mi> </munderover> <mfrac> <mrow> <msup> <mrow> <mo> ( </mo> <mfrac> <mi> b </mi> <mrow> <mi> a </mi> <mo> + </mo> <mi> b </mi> </mrow> </mfrac> <mo> ) </mo> </mrow> <mi> m </mi> </msup> <mo> 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2001-10-29