Integrate[z^4 Cosh[a Sqrt[z]], z] == (1/a^10) (2 (-9 (40320 + 20160 a^2 z + 1680 a^4 z^2 + 56 a^6 z^3 + a^8 z^4) Cosh[a Sqrt[z]] + a Sqrt[z] (362880 + 60480 a^2 z + 3024 a^4 z^2 + 72 a^6 z^3 + a^8 z^4) Sinh[a Sqrt[z]]))

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</mo> <msup> <mi> a </mi> <mn> 6 </mn> </msup> </mrow> <mo> + </mo> <mrow> <mn> 3024 </mn> <mo> &#8290; </mo> <msup> <mi> z </mi> <mn> 2 </mn> </msup> <mo> &#8290; </mo> <msup> <mi> a </mi> <mn> 4 </mn> </msup> </mrow> <mo> + </mo> <mrow> <mn> 60480 </mn> <mo> &#8290; </mo> <mi> z </mi> <mo> &#8290; </mo> <msup> <mi> a </mi> <mn> 2 </mn> </msup> </mrow> <mo> + </mo> <mn> 362880 </mn> </mrow> <mo> ) </mo> </mrow> <mo> &#8290; </mo> <mrow> <mi> sinh </mi> <mo> &#8289; </mo> <mo> ( </mo> <mrow> <mi> a </mi> <mo> &#8290; </mo> <msqrt> <mi> z </mi> </msqrt> </mrow> <mo> ) </mo> </mrow> </mrow> <mo> - </mo> <mrow> <mn> 9 </mn> <mo> &#8290; </mo> <mrow> <mo> ( </mo> <mrow> <mrow> <msup> <mi> z </mi> <mn> 4 </mn> </msup> <mo> &#8290; </mo> <msup> <mi> a </mi> <mn> 8 </mn> </msup> </mrow> <mo> + </mo> <mrow> <mn> 56 </mn> <mo> &#8290; </mo> <msup> <mi> z </mi> <mn> 3 </mn> </msup> <mo> &#8290; </mo> <msup> <mi> a </mi> <mn> 6 </mn> </msup> </mrow> <mo> + </mo> <mrow> <mn> 1680 </mn> <mo> &#8290; 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2002-12-18