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http://functions.wolfram.com/01.09.21.0158.01
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Integrate[Cot[c z]^8, z] == (1/(105 c))
(105 c z + Cot[c z] (176 - 122 Csc[c z]^2 + 66 Csc[c z]^4 - 15 Csc[c z]^6))
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Cell[BoxData[RowBox[List[RowBox[List["\[Integral]", RowBox[List[SuperscriptBox[RowBox[List["Cot", "[", RowBox[List["c", " ", "z"]], "]"]], "8"], RowBox[List["\[DifferentialD]", "z"]]]]]], "\[Equal]", RowBox[List[FractionBox["1", RowBox[List["105", " ", "c"]]], RowBox[List["(", RowBox[List[RowBox[List["105", " ", "c", " ", "z"]], "+", RowBox[List[RowBox[List["Cot", "[", RowBox[List["c", " ", "z"]], "]"]], " ", RowBox[List["(", RowBox[List["176", "-", RowBox[List["122", " ", SuperscriptBox[RowBox[List["Csc", "[", RowBox[List["c", " ", "z"]], "]"]], "2"]]], "+", RowBox[List["66", " ", SuperscriptBox[RowBox[List["Csc", "[", RowBox[List["c", " ", "z"]], "]"]], "4"]]], "-", RowBox[List["15", " ", SuperscriptBox[RowBox[List["Csc", "[", RowBox[List["c", " ", "z"]], "]"]], "6"]]]]], ")"]]]]]], ")"]]]]]]]]
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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> cot </mi> <mn> 8 </mn> </msup> <mo> ( </mo> <mrow> <mi> c </mi> <mo> ⁢ </mo> <mi> z </mi> </mrow> <mo> ) </mo> </mrow> <mo> ⁢ </mo> <mrow> <mo> ⅆ </mo> <mi> z </mi> </mrow> </mrow> </mrow> <mo> ⩵ </mo> <mfrac> <mrow> <mrow> <mn> 105 </mn> <mo> ⁢ </mo> <mi> c </mi> <mo> ⁢ </mo> <mi> z </mi> </mrow> <mo> + </mo> <mrow> <mrow> <mi> cot </mi> <mo> ⁡ </mo> <mo> ( </mo> <mrow> <mi> c </mi> <mo> ⁢ </mo> <mi> z </mi> </mrow> <mo> ) </mo> </mrow> <mo> ⁢ </mo> <mrow> <mo> ( </mo> <mrow> <mrow> <mrow> <mo> - </mo> <mn> 15 </mn> </mrow> <mo> ⁢ </mo> <mrow> <msup> <mi> csc </mi> <mn> 6 </mn> </msup> <mo> ( </mo> <mrow> <mi> c </mi> <mo> ⁢ </mo> <mi> z </mi> </mrow> <mo> ) </mo> </mrow> </mrow> <mo> + </mo> <mrow> <mn> 66 </mn> <mo> ⁢ </mo> <mrow> <msup> <mi> csc </mi> <mn> 4 </mn> </msup> <mo> ( </mo> <mrow> <mi> c </mi> <mo> ⁢ </mo> <mi> z </mi> </mrow> <mo> ) </mo> </mrow> </mrow> <mo> - </mo> <mrow> <mn> 122 </mn> <mo> ⁢ </mo> <mrow> <msup> <mi> csc </mi> <mn> 2 </mn> </msup> <mo> ( </mo> <mrow> <mi> c </mi> <mo> ⁢ </mo> <mi> z </mi> </mrow> <mo> ) </mo> </mrow> </mrow> <mo> + </mo> <mn> 176 </mn> </mrow> <mo> ) </mo> </mrow> </mrow> </mrow> <mrow> <mn> 105 </mn> <mo> ⁢ </mo> <mi> c </mi> </mrow> </mfrac> </mrow> <annotation-xml encoding='MathML-Content'> <apply> <eq /> <apply> <int /> <bvar> <ci> z </ci> </bvar> <apply> <power /> <apply> <cot /> <apply> <times /> <ci> c </ci> <ci> z </ci> </apply> </apply> <cn type='integer'> 8 </cn> </apply> </apply> <apply> <times /> <apply> <plus /> <apply> <times /> <cn type='integer'> 105 </cn> <ci> c </ci> <ci> z </ci> </apply> <apply> <times /> <apply> <cot /> <apply> <times /> <ci> c </ci> <ci> z </ci> </apply> </apply> <apply> <plus /> <apply> <times /> <cn type='integer'> -15 </cn> <apply> <power /> <apply> <csc /> <apply> <times /> <ci> c </ci> <ci> z </ci> </apply> </apply> <cn type='integer'> 6 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> 66 </cn> <apply> <power /> <apply> <csc /> <apply> <times /> <ci> c </ci> <ci> z </ci> </apply> </apply> <cn type='integer'> 4 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <cn type='integer'> 122 </cn> <apply> <power /> <apply> <csc /> <apply> <times /> <ci> c </ci> <ci> z </ci> </apply> </apply> <cn type='integer'> 2 </cn> </apply> </apply> </apply> <cn type='integer'> 176 </cn> </apply> </apply> </apply> <apply> <power /> <apply> <times /> <cn type='integer'> 105 </cn> <ci> c </ci> </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[SuperscriptBox[RowBox[List["Cot", "[", RowBox[List["c_", " ", "z_"]], "]"]], "8"], RowBox[List["\[DifferentialD]", "z_"]]]]]], "]"]], "\[RuleDelayed]", FractionBox[RowBox[List[RowBox[List["105", " ", "c", " ", "z"]], "+", RowBox[List[RowBox[List["Cot", "[", RowBox[List["c", " ", "z"]], "]"]], " ", RowBox[List["(", RowBox[List["176", "-", RowBox[List["122", " ", SuperscriptBox[RowBox[List["Csc", "[", RowBox[List["c", " ", "z"]], "]"]], "2"]]], "+", RowBox[List["66", " ", SuperscriptBox[RowBox[List["Csc", "[", RowBox[List["c", " ", "z"]], "]"]], "4"]]], "-", RowBox[List["15", " ", SuperscriptBox[RowBox[List["Csc", "[", RowBox[List["c", " ", "z"]], "]"]], "6"]]]]], ")"]]]]]], RowBox[List["105", " ", "c"]]]]]]] |
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Date Added to functions.wolfram.com (modification date)
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