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http://functions.wolfram.com/01.20.21.4127.01
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Integrate[Sinh[z]^4 Cosh[z]^6, z] ==
(120 z + 20 Sinh[2 z] - 40 Sinh[4 z] - 10 Sinh[6 z] + 5 Sinh[8 z] +
2 Sinh[10 z])/10240
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Cell[BoxData[RowBox[List[RowBox[List["\[Integral]", RowBox[List[SuperscriptBox[RowBox[List["Sinh", "[", "z", "]"]], "4"], SuperscriptBox[RowBox[List["Cosh", "[", "z", "]"]], "6"], " ", RowBox[List["\[DifferentialD]", "z"]]]]]], "\[Equal]", FractionBox[RowBox[List[RowBox[List["120", " ", "z"]], "+", RowBox[List["20", " ", RowBox[List["Sinh", "[", RowBox[List["2", " ", "z"]], "]"]]]], "-", RowBox[List["40", " ", RowBox[List["Sinh", "[", RowBox[List["4", " ", "z"]], "]"]]]], "-", RowBox[List["10", " ", RowBox[List["Sinh", "[", RowBox[List["6", " ", "z"]], "]"]]]], "+", RowBox[List["5", " ", RowBox[List["Sinh", "[", RowBox[List["8", " ", "z"]], "]"]]]], "+", RowBox[List["2", " ", RowBox[List["Sinh", "[", RowBox[List["10", " ", "z"]], "]"]]]]]], "10240"]]]]]
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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> sinh </mi> <mn> 4 </mn> </msup> <mo> ( </mo> <mi> z </mi> <mo> ) </mo> </mrow> <mo> ⁢ </mo> <mrow> <msup> <mi> cosh </mi> <mn> 6 </mn> </msup> <mo> ( </mo> <mi> z </mi> <mo> ) </mo> </mrow> <mo> ⁢ </mo> <mrow> <mo> ⅆ </mo> <mi> z </mi> </mrow> </mrow> </mrow> <mo> ⩵ </mo> <mfrac> <mrow> <mrow> <mn> 120 </mn> <mo> ⁢ </mo> <mi> z </mi> </mrow> <mo> + </mo> <mrow> <mn> 20 </mn> <mo> ⁢ </mo> <mrow> <mi> sinh </mi> <mo> ⁡ </mo> <mo> ( </mo> <mrow> <mn> 2 </mn> <mo> ⁢ </mo> <mi> z </mi> </mrow> <mo> ) </mo> </mrow> </mrow> <mo> - </mo> <mrow> <mn> 40 </mn> <mo> ⁢ </mo> <mrow> <mi> sinh </mi> <mo> ⁡ </mo> <mo> ( </mo> <mrow> <mn> 4 </mn> <mo> ⁢ </mo> <mi> z </mi> </mrow> <mo> ) </mo> </mrow> </mrow> <mo> - </mo> <mrow> <mn> 10 </mn> <mo> ⁢ </mo> <mrow> <mi> sinh </mi> <mo> ⁡ </mo> <mo> ( </mo> <mrow> <mn> 6 </mn> <mo> ⁢ </mo> <mi> z </mi> </mrow> <mo> ) </mo> </mrow> </mrow> <mo> + </mo> <mrow> <mn> 5 </mn> <mo> ⁢ </mo> <mrow> <mi> sinh </mi> <mo> ⁡ </mo> <mo> ( </mo> <mrow> <mn> 8 </mn> <mo> ⁢ </mo> <mi> z </mi> </mrow> <mo> ) </mo> </mrow> </mrow> <mo> + </mo> <mrow> <mn> 2 </mn> <mo> ⁢ </mo> <mrow> <mi> sinh </mi> <mo> ⁡ </mo> <mo> ( </mo> <mrow> <mn> 10 </mn> <mo> ⁢ </mo> <mi> z </mi> </mrow> <mo> ) </mo> </mrow> </mrow> </mrow> <mn> 10240 </mn> </mfrac> </mrow> <annotation-xml encoding='MathML-Content'> <apply> <eq /> <apply> <int /> <bvar> <ci> z </ci> </bvar> <apply> <times /> <apply> <power /> <apply> <sinh /> <ci> z </ci> </apply> <cn type='integer'> 4 </cn> </apply> <apply> <power /> <apply> <cosh /> <ci> z </ci> </apply> <cn type='integer'> 6 </cn> </apply> </apply> </apply> <apply> <times /> <apply> <plus /> <apply> <times /> <cn type='integer'> 120 </cn> <ci> z </ci> </apply> <apply> <times /> <cn type='integer'> 20 </cn> <apply> <sinh /> <apply> <times /> <cn type='integer'> 2 </cn> <ci> z </ci> </apply> </apply> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <cn type='integer'> 40 </cn> <apply> <sinh /> <apply> <times /> <cn type='integer'> 4 </cn> <ci> z </ci> </apply> </apply> </apply> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <cn type='integer'> 10 </cn> <apply> <sinh /> <apply> <times /> <cn type='integer'> 6 </cn> <ci> z </ci> </apply> </apply> </apply> </apply> <apply> <times /> <cn type='integer'> 5 </cn> <apply> <sinh /> <apply> <times /> <cn type='integer'> 8 </cn> <ci> z </ci> </apply> </apply> </apply> <apply> <times /> <cn type='integer'> 2 </cn> <apply> <sinh /> <apply> <times /> <cn type='integer'> 10 </cn> <ci> z </ci> </apply> </apply> </apply> </apply> <apply> <power /> <cn type='integer'> 10240 </cn> <cn type='integer'> -1 </cn> </apply> </apply> </apply> </annotation-xml> </semantics> </math>
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| Cell[BoxData[RowBox[List[RowBox[List["HoldPattern", "[", RowBox[List["\[Integral]", RowBox[List[RowBox[List[SuperscriptBox[RowBox[List["Sinh", "[", "z_", "]"]], "4"], " ", SuperscriptBox[RowBox[List["Cosh", "[", "z_", "]"]], "6"]]], RowBox[List["\[DifferentialD]", "z_"]]]]]], "]"]], "\[RuleDelayed]", FractionBox[RowBox[List[RowBox[List["120", " ", "z"]], "+", RowBox[List["20", " ", RowBox[List["Sinh", "[", RowBox[List["2", " ", "z"]], "]"]]]], "-", RowBox[List["40", " ", RowBox[List["Sinh", "[", RowBox[List["4", " ", "z"]], "]"]]]], "-", RowBox[List["10", " ", RowBox[List["Sinh", "[", RowBox[List["6", " ", "z"]], "]"]]]], "+", RowBox[List["5", " ", RowBox[List["Sinh", "[", RowBox[List["8", " ", "z"]], "]"]]]], "+", RowBox[List["2", " ", RowBox[List["Sinh", "[", RowBox[List["10", " ", "z"]], "]"]]]]]], "10240"]]]]] |
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Date Added to functions.wolfram.com (modification date)
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