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http://functions.wolfram.com/01.20.21.0132.01
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Integrate[z^5 Cosh[a Sqrt[z] + b], z] ==
(1/a^12) (2 (-11 (3628800 + 1814400 a^2 z + 151200 a^4 z^2 + 5040 a^6 z^3 +
90 a^8 z^4 + a^10 z^5) Cosh[b + a Sqrt[z]] +
a Sqrt[z] (39916800 + 6652800 a^2 z + 332640 a^4 z^2 + 7920 a^6 z^3 +
110 a^8 z^4 + a^10 z^5) Sinh[b + a Sqrt[z]]))
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Cell[BoxData[RowBox[List[RowBox[List["\[Integral]", RowBox[List[SuperscriptBox["z", "5"], " ", RowBox[List["Cosh", "[", RowBox[List[RowBox[List["a", " ", SqrtBox["z"]]], "+", "b"]], "]"]], RowBox[List["\[DifferentialD]", "z"]]]]]], "\[Equal]", RowBox[List[FractionBox["1", SuperscriptBox["a", "12"]], RowBox[List["(", RowBox[List["2", " ", RowBox[List["(", RowBox[List[RowBox[List[RowBox[List["-", "11"]], " ", RowBox[List["(", RowBox[List["3628800", "+", RowBox[List["1814400", " ", SuperscriptBox["a", "2"], " ", "z"]], "+", RowBox[List["151200", " ", SuperscriptBox["a", "4"], " ", SuperscriptBox["z", "2"]]], "+", RowBox[List["5040", " ", SuperscriptBox["a", "6"], " ", SuperscriptBox["z", "3"]]], "+", RowBox[List["90", " ", SuperscriptBox["a", "8"], " ", SuperscriptBox["z", "4"]]], "+", RowBox[List[SuperscriptBox["a", "10"], " ", SuperscriptBox["z", "5"]]]]], ")"]], " ", RowBox[List["Cosh", "[", RowBox[List["b", "+", RowBox[List["a", " ", SqrtBox["z"]]]]], "]"]]]], "+", RowBox[List["a", " ", SqrtBox["z"], " ", RowBox[List["(", RowBox[List["39916800", "+", RowBox[List["6652800", " ", SuperscriptBox["a", "2"], " ", "z"]], "+", RowBox[List["332640", " ", SuperscriptBox["a", "4"], " ", SuperscriptBox["z", "2"]]], "+", RowBox[List["7920", " ", SuperscriptBox["a", "6"], " ", SuperscriptBox["z", "3"]]], "+", RowBox[List["110", " ", SuperscriptBox["a", "8"], " ", SuperscriptBox["z", "4"]]], "+", RowBox[List[SuperscriptBox["a", "10"], " ", SuperscriptBox["z", "5"]]]]], ")"]], " ", RowBox[List["Sinh", "[", RowBox[List["b", "+", RowBox[List["a", " ", SqrtBox["z"]]]]], "]"]]]]]], ")"]]]], ")"]]]]]]]]
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<math xmlns='http://www.w3.org/1998/Math/MathML' mathematica:form='TraditionalForm' xmlns:mathematica='http://www.wolfram.com/XML/'> <semantics> <mrow> <mrow> <mo> ∫ </mo> <mrow> <mrow> <msup> <mi> z </mi> <mn> 5 </mn> </msup> <mo> ⁢ </mo> <mrow> <mi> cosh </mi> <mo> ⁡ </mo> <mo> ( </mo> <mrow> <mrow> <msqrt> <mi> z </mi> </msqrt> <mo> ⁢ </mo> <mi> a </mi> </mrow> <mo> + </mo> <mi> b </mi> </mrow> <mo> ) </mo> </mrow> </mrow> <mo> ⁢ </mo> <mrow> <mo> ⅆ </mo> <mi> z </mi> </mrow> </mrow> </mrow> <mo> ⩵ </mo> <mrow> <mfrac> <mn> 1 </mn> <msup> <mi> a </mi> <mn> 12 </mn> </msup> </mfrac> <mo> ⁢ </mo> <mrow> <mo> ( </mo> <mrow> <mn> 2 </mn> <mo> ⁢ </mo> <mrow> <mo> ( </mo> <mrow> <mrow> <mi> a </mi> <mo> ⁢ </mo> <msqrt> <mi> z </mi> </msqrt> <mo> ⁢ </mo> <mrow> <mo> ( </mo> <mrow> <mrow> <msup> <mi> z </mi> <mn> 5 </mn> </msup> <mo> ⁢ </mo> <msup> <mi> a </mi> <mn> 10 </mn> </msup> </mrow> <mo> + </mo> <mrow> <mn> 110 </mn> <mo> ⁢ </mo> <msup> <mi> z </mi> <mn> 4 </mn> </msup> <mo> ⁢ </mo> <msup> <mi> a </mi> <mn> 8 </mn> </msup> </mrow> <mo> + </mo> <mrow> <mn> 7920 </mn> <mo> ⁢ </mo> <msup> <mi> z </mi> <mn> 3 </mn> </msup> <mo> ⁢ </mo> <msup> <mi> a </mi> <mn> 6 </mn> </msup> </mrow> <mo> + </mo> <mrow> <mn> 332640 </mn> <mo> ⁢ </mo> <msup> <mi> z </mi> <mn> 2 </mn> </msup> <mo> ⁢ </mo> <msup> <mi> a </mi> <mn> 4 </mn> </msup> </mrow> <mo> + </mo> <mrow> <mn> 6652800 </mn> <mo> ⁢ </mo> <mi> z </mi> <mo> ⁢ </mo> <msup> <mi> a </mi> <mn> 2 </mn> </msup> </mrow> <mo> + </mo> <mn> 39916800 </mn> </mrow> <mo> ) </mo> </mrow> <mo> ⁢ </mo> <mrow> <mi> sinh </mi> <mo> ⁡ </mo> <mo> ( </mo> <mrow> <mrow> <msqrt> <mi> z </mi> </msqrt> <mo> ⁢ </mo> <mi> a </mi> </mrow> <mo> + </mo> <mi> b </mi> </mrow> <mo> ) </mo> </mrow> </mrow> <mo> - </mo> <mrow> <mn> 11 </mn> <mo> ⁢ </mo> <mrow> <mo> ( </mo> <mrow> <mrow> <msup> <mi> z </mi> <mn> 5 </mn> </msup> <mo> ⁢ </mo> <msup> <mi> a </mi> <mn> 10 </mn> </msup> </mrow> <mo> + </mo> <mrow> <mn> 90 </mn> <mo> ⁢ </mo> <msup> <mi> z </mi> <mn> 4 </mn> </msup> <mo> ⁢ </mo> <msup> <mi> a </mi> <mn> 8 </mn> </msup> </mrow> <mo> + </mo> <mrow> <mn> 5040 </mn> <mo> ⁢ </mo> <msup> <mi> z </mi> <mn> 3 </mn> </msup> <mo> ⁢ </mo> <msup> <mi> a </mi> <mn> 6 </mn> </msup> </mrow> <mo> + </mo> <mrow> <mn> 151200 </mn> <mo> ⁢ </mo> <msup> <mi> z </mi> <mn> 2 </mn> </msup> <mo> ⁢ </mo> <msup> <mi> a </mi> <mn> 4 </mn> </msup> </mrow> <mo> + </mo> <mrow> <mn> 1814400 </mn> <mo> ⁢ </mo> <mi> z </mi> <mo> ⁢ </mo> <msup> <mi> a </mi> <mn> 2 </mn> </msup> </mrow> <mo> + </mo> <mn> 3628800 </mn> </mrow> <mo> ) </mo> </mrow> <mo> ⁢ </mo> <mrow> <mi> cosh </mi> <mo> ⁡ </mo> <mo> ( </mo> <mrow> <mrow> <msqrt> <mi> z </mi> </msqrt> <mo> ⁢ </mo> <mi> a </mi> </mrow> <mo> + </mo> <mi> b </mi> </mrow> <mo> ) </mo> </mrow> </mrow> </mrow> <mo> ) </mo> </mrow> </mrow> <mo> ) </mo> </mrow> </mrow> </mrow> <annotation-xml encoding='MathML-Content'> <apply> <eq /> <apply> <int /> <bvar> <ci> z </ci> </bvar> <apply> <times /> <apply> <power /> <ci> z </ci> <cn type='integer'> 5 </cn> </apply> <apply> <cosh /> <apply> <plus /> <apply> <times /> <apply> <power /> <ci> z </ci> <cn type='rational'> 1 <sep /> 2 </cn> </apply> <ci> a </ci> </apply> <ci> b </ci> </apply> </apply> </apply> </apply> <apply> <times /> <apply> <times /> <cn type='integer'> 1 </cn> <apply> <power /> <apply> <power /> <ci> a </ci> <cn type='integer'> 12 </cn> </apply> <cn type='integer'> -1 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> 2 </cn> <apply> <plus /> <apply> <times /> <ci> a </ci> <apply> <power /> <ci> z </ci> <cn type='rational'> 1 <sep /> 2 </cn> </apply> <apply> <plus /> <apply> <times /> <apply> <power /> <ci> z </ci> <cn type='integer'> 5 </cn> </apply> <apply> <power /> <ci> a </ci> <cn type='integer'> 10 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> 110 </cn> <apply> <power /> <ci> z </ci> <cn type='integer'> 4 </cn> </apply> <apply> <power /> <ci> a </ci> <cn type='integer'> 8 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> 7920 </cn> <apply> <power /> <ci> z </ci> <cn type='integer'> 3 </cn> </apply> <apply> <power /> <ci> a </ci> <cn type='integer'> 6 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> 332640 </cn> <apply> <power /> <ci> z </ci> <cn type='integer'> 2 </cn> </apply> <apply> <power /> <ci> a </ci> <cn type='integer'> 4 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> 6652800 </cn> <ci> z </ci> <apply> <power /> <ci> a </ci> <cn type='integer'> 2 </cn> </apply> </apply> <cn type='integer'> 39916800 </cn> </apply> <apply> <sinh /> <apply> <plus /> <apply> <times /> <apply> <power /> <ci> z </ci> <cn type='rational'> 1 <sep /> 2 </cn> </apply> <ci> a </ci> </apply> <ci> b </ci> </apply> </apply> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <cn type='integer'> 11 </cn> <apply> <plus /> <apply> <times /> <apply> <power /> <ci> z </ci> <cn type='integer'> 5 </cn> </apply> <apply> <power /> <ci> a </ci> <cn type='integer'> 10 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> 90 </cn> <apply> <power /> <ci> z </ci> <cn type='integer'> 4 </cn> </apply> <apply> <power /> <ci> a </ci> <cn type='integer'> 8 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> 5040 </cn> <apply> <power /> <ci> z </ci> <cn type='integer'> 3 </cn> </apply> <apply> <power /> <ci> a </ci> <cn type='integer'> 6 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> 151200 </cn> <apply> <power /> <ci> z </ci> <cn type='integer'> 2 </cn> </apply> <apply> <power /> <ci> a </ci> <cn type='integer'> 4 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> 1814400 </cn> <ci> z </ci> <apply> <power /> <ci> a </ci> <cn type='integer'> 2 </cn> </apply> </apply> <cn type='integer'> 3628800 </cn> </apply> <apply> <cosh /> <apply> <plus /> <apply> <times /> <apply> <power /> <ci> z </ci> <cn type='rational'> 1 <sep /> 2 </cn> </apply> <ci> a </ci> </apply> <ci> b </ci> </apply> </apply> </apply> </apply> </apply> </apply> </apply> </apply> </annotation-xml> </semantics> </math>
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Date Added to functions.wolfram.com (modification date)
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){kind=small}
