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http://functions.wolfram.com/01.24.21.0431.01
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Integrate[Csch[z]^4 Sech[z]^2, z] == (-(1/3)) Coth[z] (-5 + Csch[z]^2) +
Tanh[z]
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Cell[BoxData[RowBox[List[RowBox[List["\[Integral]", RowBox[List[RowBox[List[SuperscriptBox[RowBox[List["Csch", "[", "z", "]"]], "4"], " ", SuperscriptBox[RowBox[List["Sech", "[", "z", "]"]], "2"]]], RowBox[List["\[DifferentialD]", "z"]]]]]], "\[Equal]", RowBox[List[RowBox[List[RowBox[List["-", FractionBox["1", "3"]]], " ", RowBox[List["Coth", "[", "z", "]"]], " ", RowBox[List["(", RowBox[List[RowBox[List["-", "5"]], "+", SuperscriptBox[RowBox[List["Csch", "[", "z", "]"]], "2"]]], ")"]]]], "+", RowBox[List["Tanh", "[", "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> <mrow> <msup> <mi> csch </mi> <mn> 4 </mn> </msup> <mo> ( </mo> <mi> z </mi> <mo> ) </mo> </mrow> <mo> ⁢ </mo> <mrow> <msup> <mi> sech </mi> <mn> 2 </mn> </msup> <mo> ( </mo> <mi> z </mi> <mo> ) </mo> </mrow> </mrow> <mo> ⁢ </mo> <mrow> <mo> ⅆ </mo> <mi> z </mi> </mrow> </mrow> </mrow> <mo> ⩵ </mo> <mrow> <mrow> <mi> tanh </mi> <mo> ⁡ </mo> <mo> ( </mo> <mi> z </mi> <mo> ) </mo> </mrow> <mo> - </mo> <mrow> <mfrac> <mn> 1 </mn> <mn> 3 </mn> </mfrac> <mo> ⁢ </mo> <mrow> <mi> coth </mi> <mo> ⁡ </mo> <mo> ( </mo> <mi> z </mi> <mo> ) </mo> </mrow> <mo> ⁢ </mo> <mrow> <mo> ( </mo> <mrow> <mrow> <msup> <mi> csch </mi> <mn> 2 </mn> </msup> <mo> ( </mo> <mi> z </mi> <mo> ) </mo> </mrow> <mo> - </mo> <mn> 5 </mn> </mrow> <mo> ) </mo> </mrow> </mrow> </mrow> </mrow> <annotation-xml encoding='MathML-Content'> <apply> <eq /> <apply> <int /> <bvar> <ci> z </ci> </bvar> <apply> <times /> <apply> <power /> <apply> <csch /> <ci> z </ci> </apply> <cn type='integer'> 4 </cn> </apply> <apply> <power /> <apply> <sech /> <ci> z </ci> </apply> <cn type='integer'> 2 </cn> </apply> </apply> </apply> <apply> <plus /> <apply> <tanh /> <ci> z </ci> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <cn type='rational'> 1 <sep /> 3 </cn> <apply> <coth /> <ci> z </ci> </apply> <apply> <plus /> <apply> <power /> <apply> <csch /> <ci> z </ci> </apply> <cn type='integer'> 2 </cn> </apply> <cn type='integer'> -5 </cn> </apply> </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[SuperscriptBox[RowBox[List["Csch", "[", "z_", "]"]], "4"], " ", SuperscriptBox[RowBox[List["Sech", "[", "z_", "]"]], "2"]]], RowBox[List["\[DifferentialD]", "z_"]]]]]], "]"]], "\[RuleDelayed]", RowBox[List[RowBox[List[RowBox[List["-", FractionBox["1", "3"]]], " ", RowBox[List["Coth", "[", "z", "]"]], " ", RowBox[List["(", RowBox[List[RowBox[List["-", "5"]], "+", SuperscriptBox[RowBox[List["Csch", "[", "z", "]"]], "2"]]], ")"]]]], "+", RowBox[List["Tanh", "[", "z", "]"]]]]]]]] |
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Date Added to functions.wolfram.com (modification date)
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