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http://functions.wolfram.com/01.24.21.0415.01
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Integrate[Tanh[z]^5 Sqrt[Sech[z]^3], z] == (-(2/231)) Sqrt[Sech[z]^3]
(77 - 66 Sech[z]^2 + 21 Sech[z]^4)
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Cell[BoxData[RowBox[List[RowBox[List["\[Integral]", " ", RowBox[List[SuperscriptBox[RowBox[List["Tanh", "[", "z", "]"]], "5"], SqrtBox[SuperscriptBox[RowBox[List["Sech", "[", "z", "]"]], "3"]], RowBox[List["\[DifferentialD]", "z"]]]]]], "\[Equal]", RowBox[List[RowBox[List["-", FractionBox["2", "231"]]], " ", SqrtBox[SuperscriptBox[RowBox[List["Sech", "[", "z", "]"]], "3"]], " ", RowBox[List["(", RowBox[List["77", "-", RowBox[List["66", " ", SuperscriptBox[RowBox[List["Sech", "[", "z", "]"]], "2"]]], "+", RowBox[List["21", " ", SuperscriptBox[RowBox[List["Sech", "[", "z", "]"]], "4"]]]]], ")"]]]]]]]]
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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> <mtext> </mtext> <mrow> <mrow> <msup> <mi> tanh </mi> <mn> 5 </mn> </msup> <mo> ( </mo> <mi> z </mi> <mo> ) </mo> </mrow> <mo> ⁢ </mo> <msqrt> <mrow> <msup> <mi> sech </mi> <mn> 3 </mn> </msup> <mo> ( </mo> <mi> z </mi> <mo> ) </mo> </mrow> </msqrt> <mo> ⁢ </mo> <mrow> <mo> ⅆ </mo> <mi> z </mi> </mrow> </mrow> </mrow> <mo> ⩵ </mo> <mrow> <mrow> <mo> - </mo> <mfrac> <mn> 2 </mn> <mn> 231 </mn> </mfrac> </mrow> <mo> ⁢ </mo> <msqrt> <mrow> <msup> <mi> sech </mi> <mn> 3 </mn> </msup> <mo> ( </mo> <mi> z </mi> <mo> ) </mo> </mrow> </msqrt> <mo> ⁢ </mo> <mrow> <mo> ( </mo> <mrow> <mrow> <mn> 21 </mn> <mo> ⁢ </mo> <mrow> <msup> <mi> sech </mi> <mn> 4 </mn> </msup> <mo> ( </mo> <mi> z </mi> <mo> ) </mo> </mrow> </mrow> <mo> - </mo> <mrow> <mn> 66 </mn> <mo> ⁢ </mo> <mrow> <msup> <mi> sech </mi> <mn> 2 </mn> </msup> <mo> ( </mo> <mi> z </mi> <mo> ) </mo> </mrow> </mrow> <mo> + </mo> <mn> 77 </mn> </mrow> <mo> ) </mo> </mrow> </mrow> </mrow> <annotation-xml encoding='MathML-Content'> <apply> <eq /> <apply> <int /> <bvar> <ci> z </ci> </bvar> <apply> <times /> <apply> <power /> <apply> <tanh /> <ci> z </ci> </apply> <cn type='integer'> 5 </cn> </apply> <apply> <power /> <apply> <power /> <apply> <sech /> <ci> z </ci> </apply> <cn type='integer'> 3 </cn> </apply> <cn type='rational'> 1 <sep /> 2 </cn> </apply> </apply> </apply> <apply> <times /> <apply> <times /> <cn type='integer'> -1 </cn> <cn type='rational'> 2 <sep /> 231 </cn> </apply> <apply> <power /> <apply> <power /> <apply> <sech /> <ci> z </ci> </apply> <cn type='integer'> 3 </cn> </apply> <cn type='rational'> 1 <sep /> 2 </cn> </apply> <apply> <plus /> <apply> <times /> <cn type='integer'> 21 </cn> <apply> <power /> <apply> <sech /> <ci> z </ci> </apply> <cn type='integer'> 4 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <cn type='integer'> 66 </cn> <apply> <power /> <apply> <sech /> <ci> z </ci> </apply> <cn type='integer'> 2 </cn> </apply> </apply> </apply> <cn type='integer'> 77 </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["Tanh", "[", "z_", "]"]], "5"], " ", SqrtBox[SuperscriptBox[RowBox[List["Sech", "[", "z_", "]"]], "3"]]]], RowBox[List["\[DifferentialD]", "z_"]]]]]], "]"]], "\[RuleDelayed]", RowBox[List[FractionBox["1", "231"], " ", RowBox[List["(", RowBox[List["-", "2"]], ")"]], " ", SqrtBox[SuperscriptBox[RowBox[List["Sech", "[", "z", "]"]], "3"]], " ", RowBox[List["(", RowBox[List["77", "-", RowBox[List["66", " ", SuperscriptBox[RowBox[List["Sech", "[", "z", "]"]], "2"]]], "+", RowBox[List["21", " ", SuperscriptBox[RowBox[List["Sech", "[", "z", "]"]], "4"]]]]], ")"]]]]]]]] |
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Date Added to functions.wolfram.com (modification date)
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