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http://functions.wolfram.com/01.19.21.1848.01
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Integrate[z Sinh[a z]^3, z] ==
-((27 a z Cosh[a z] - 3 a z Cosh[3 a z] - 27 Sinh[a z] + Sinh[3 a z])/
(36 a^2))
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Cell[BoxData[RowBox[List[RowBox[List["\[Integral]", RowBox[List["z", " ", SuperscriptBox[RowBox[List["Sinh", "[", RowBox[List["a", " ", "z"]], "]"]], "3"], RowBox[List["\[DifferentialD]", "z"]]]]]], "\[Equal]", RowBox[List["-", FractionBox[RowBox[List[RowBox[List["27", " ", "a", " ", "z", " ", RowBox[List["Cosh", "[", RowBox[List["a", " ", "z"]], "]"]]]], "-", RowBox[List["3", " ", "a", " ", "z", " ", RowBox[List["Cosh", "[", RowBox[List["3", " ", "a", " ", "z"]], "]"]]]], "-", RowBox[List["27", " ", RowBox[List["Sinh", "[", RowBox[List["a", " ", "z"]], "]"]]]], "+", RowBox[List["Sinh", "[", RowBox[List["3", " ", "a", " ", "z"]], "]"]]]], RowBox[List["36", " ", SuperscriptBox["a", "2"]]]]]]]]]]
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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> <mi> z </mi> <mo> ⁢ </mo> <mrow> <msup> <mi> sinh </mi> <mn> 3 </mn> </msup> <mo> ( </mo> <mrow> <mi> a </mi> <mo> ⁢ </mo> <mi> z </mi> </mrow> <mo> ) </mo> </mrow> <mo> ⁢ </mo> <mrow> <mo> ⅆ </mo> <mi> z </mi> </mrow> </mrow> </mrow> <mo> ⩵ </mo> <mrow> <mo> - </mo> <mfrac> <mrow> <mrow> <mn> 27 </mn> <mo> ⁢ </mo> <mi> a </mi> <mo> ⁢ </mo> <mi> z </mi> <mo> ⁢ </mo> <mrow> <mi> cosh </mi> <mo> ⁡ </mo> <mo> ( </mo> <mrow> <mi> a </mi> <mo> ⁢ </mo> <mi> z </mi> </mrow> <mo> ) </mo> </mrow> </mrow> <mo> - </mo> <mrow> <mn> 3 </mn> <mo> ⁢ </mo> <mi> a </mi> <mo> ⁢ </mo> <mi> z </mi> <mo> ⁢ </mo> <mrow> <mi> cosh </mi> <mo> ⁡ </mo> <mo> ( </mo> <mrow> <mn> 3 </mn> <mo> ⁢ </mo> <mi> a </mi> <mo> ⁢ </mo> <mi> z </mi> </mrow> <mo> ) </mo> </mrow> </mrow> <mo> - </mo> <mrow> <mn> 27 </mn> <mo> ⁢ </mo> <mrow> <mi> sinh </mi> <mo> ⁡ </mo> <mo> ( </mo> <mrow> <mi> a </mi> <mo> ⁢ </mo> <mi> z </mi> </mrow> <mo> ) </mo> </mrow> </mrow> <mo> + </mo> <mrow> <mi> sinh </mi> <mo> ⁡ </mo> <mo> ( </mo> <mrow> <mn> 3 </mn> <mo> ⁢ </mo> <mi> a </mi> <mo> ⁢ </mo> <mi> z </mi> </mrow> <mo> ) </mo> </mrow> </mrow> <mrow> <mn> 36 </mn> <mo> ⁢ </mo> <msup> <mi> a </mi> <mn> 2 </mn> </msup> </mrow> </mfrac> </mrow> </mrow> <annotation-xml encoding='MathML-Content'> <apply> <eq /> <apply> <int /> <bvar> <ci> z </ci> </bvar> <apply> <times /> <ci> z </ci> <apply> <power /> <apply> <sinh /> <apply> <times /> <ci> a </ci> <ci> z </ci> </apply> </apply> <cn type='integer'> 3 </cn> </apply> </apply> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <apply> <plus /> <apply> <times /> <cn type='integer'> 27 </cn> <ci> a </ci> <ci> z </ci> <apply> <cosh /> <apply> <times /> <ci> a </ci> <ci> z </ci> </apply> </apply> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <cn type='integer'> 3 </cn> <ci> a </ci> <ci> z </ci> <apply> <cosh /> <apply> <times /> <cn type='integer'> 3 </cn> <ci> a </ci> <ci> z </ci> </apply> </apply> </apply> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <cn type='integer'> 27 </cn> <apply> <sinh /> <apply> <times /> <ci> a </ci> <ci> z </ci> </apply> </apply> </apply> </apply> <apply> <sinh /> <apply> <times /> <cn type='integer'> 3 </cn> <ci> a </ci> <ci> z </ci> </apply> </apply> </apply> <apply> <power /> <apply> <times /> <cn type='integer'> 36 </cn> <apply> <power /> <ci> a </ci> <cn type='integer'> 2 </cn> </apply> </apply> <cn type='integer'> -1 </cn> </apply> </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["z_", " ", SuperscriptBox[RowBox[List["Sinh", "[", RowBox[List["a_", " ", "z_"]], "]"]], "3"]]], RowBox[List["\[DifferentialD]", "z_"]]]]]], "]"]], "\[RuleDelayed]", RowBox[List["-", FractionBox[RowBox[List[RowBox[List["27", " ", "a", " ", "z", " ", RowBox[List["Cosh", "[", RowBox[List["a", " ", "z"]], "]"]]]], "-", RowBox[List["3", " ", "a", " ", "z", " ", RowBox[List["Cosh", "[", RowBox[List["3", " ", "a", " ", "z"]], "]"]]]], "-", RowBox[List["27", " ", RowBox[List["Sinh", "[", RowBox[List["a", " ", "z"]], "]"]]]], "+", RowBox[List["Sinh", "[", RowBox[List["3", " ", "a", " ", "z"]], "]"]]]], RowBox[List["36", " ", SuperscriptBox["a", "2"]]]]]]]]]] |
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Date Added to functions.wolfram.com (modification date)
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