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http://functions.wolfram.com/01.20.21.4605.01
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Integrate[z^2/((-z) Cosh[z] + Sinh[z])^2, z] ==
(Cosh[z] - z Sinh[z])/((-z) Cosh[z] + Sinh[z])
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Cell[BoxData[RowBox[List[RowBox[List["\[Integral]", RowBox[List[FractionBox[SuperscriptBox["z", "2"], SuperscriptBox[RowBox[List["(", RowBox[List[RowBox[List[RowBox[List["-", "z"]], " ", RowBox[List["Cosh", "[", "z", "]"]]]], "+", RowBox[List["Sinh", "[", "z", "]"]]]], ")"]], "2"]], RowBox[List["\[DifferentialD]", "z"]]]]]], "\[Equal]", FractionBox[RowBox[List[RowBox[List["Cosh", "[", "z", "]"]], "-", RowBox[List["z", " ", RowBox[List["Sinh", "[", "z", "]"]]]]]], RowBox[List[RowBox[List[RowBox[List["-", "z"]], " ", RowBox[List["Cosh", "[", "z", "]"]]]], "+", RowBox[List["Sinh", "[", "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> <mfrac> <msup> <mi> z </mi> <mn> 2 </mn> </msup> <msup> <mrow> <mo> ( </mo> <mrow> <mrow> <mi> sinh </mi> <mo> ⁡ </mo> <mo> ( </mo> <mi> z </mi> <mo> ) </mo> </mrow> <mo> - </mo> <mrow> <mi> z </mi> <mo> ⁢ </mo> <mrow> <mi> cosh </mi> <mo> ⁡ </mo> <mo> ( </mo> <mi> z </mi> <mo> ) </mo> </mrow> </mrow> </mrow> <mo> ) </mo> </mrow> <mn> 2 </mn> </msup> </mfrac> <mo> ⁢ </mo> <mrow> <mo> ⅆ </mo> <mi> z </mi> </mrow> </mrow> </mrow> <mo> ⩵ </mo> <mfrac> <mrow> <mrow> <mi> cosh </mi> <mo> ⁡ </mo> <mo> ( </mo> <mi> z </mi> <mo> ) </mo> </mrow> <mo> - </mo> <mrow> <mi> z </mi> <mo> ⁢ </mo> <mrow> <mi> sinh </mi> <mo> ⁡ </mo> <mo> ( </mo> <mi> z </mi> <mo> ) </mo> </mrow> </mrow> </mrow> <mrow> <mrow> <mi> sinh </mi> <mo> ⁡ </mo> <mo> ( </mo> <mi> z </mi> <mo> ) </mo> </mrow> <mo> - </mo> <mrow> <mi> z </mi> <mo> ⁢ </mo> <mrow> <mi> cosh </mi> <mo> ⁡ </mo> <mo> ( </mo> <mi> z </mi> <mo> ) </mo> </mrow> </mrow> </mrow> </mfrac> </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'> 2 </cn> </apply> <apply> <power /> <apply> <power /> <apply> <plus /> <apply> <sinh /> <ci> z </ci> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <ci> z </ci> <apply> <cosh /> <ci> z </ci> </apply> </apply> </apply> </apply> <cn type='integer'> 2 </cn> </apply> <cn type='integer'> -1 </cn> </apply> </apply> </apply> <apply> <times /> <apply> <plus /> <apply> <cosh /> <ci> z </ci> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <ci> z </ci> <apply> <sinh /> <ci> z </ci> </apply> </apply> </apply> </apply> <apply> <power /> <apply> <plus /> <apply> <sinh /> <ci> z </ci> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <ci> z </ci> <apply> <cosh /> <ci> z </ci> </apply> </apply> </apply> </apply> <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[FractionBox[SuperscriptBox["z_", "2"], SuperscriptBox[RowBox[List["(", RowBox[List[RowBox[List[RowBox[List["-", "z_"]], " ", RowBox[List["Cosh", "[", "z_", "]"]]]], "+", RowBox[List["Sinh", "[", "z_", "]"]]]], ")"]], "2"]], RowBox[List["\[DifferentialD]", "z_"]]]]]], "]"]], "\[RuleDelayed]", FractionBox[RowBox[List[RowBox[List["Cosh", "[", "z", "]"]], "-", RowBox[List["z", " ", RowBox[List["Sinh", "[", "z", "]"]]]]]], RowBox[List[RowBox[List[RowBox[List["-", "z"]], " ", RowBox[List["Cosh", "[", "z", "]"]]]], "+", RowBox[List["Sinh", "[", "z", "]"]]]]]]]]] |
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Date Added to functions.wolfram.com (modification date)
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