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http://functions.wolfram.com/01.11.21.0083.01
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Integrate[Sec[c z]^12, z] == (1/(693 c))
((256 + 128 Sec[c z]^2 + 96 Sec[c z]^4 + 80 Sec[c z]^6 + 70 Sec[c z]^8 +
63 Sec[c z]^10) Tan[c z])
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Cell[BoxData[RowBox[List[RowBox[List["\[Integral]", RowBox[List[SuperscriptBox[RowBox[List["Sec", "[", RowBox[List["c", " ", "z"]], "]"]], "12"], RowBox[List["\[DifferentialD]", "z"]]]]]], "\[Equal]", RowBox[List[FractionBox["1", RowBox[List["693", " ", "c"]]], RowBox[List["(", RowBox[List[RowBox[List["(", RowBox[List["256", "+", RowBox[List["128", " ", SuperscriptBox[RowBox[List["Sec", "[", RowBox[List["c", " ", "z"]], "]"]], "2"]]], "+", RowBox[List["96", " ", SuperscriptBox[RowBox[List["Sec", "[", RowBox[List["c", " ", "z"]], "]"]], "4"]]], "+", RowBox[List["80", " ", SuperscriptBox[RowBox[List["Sec", "[", RowBox[List["c", " ", "z"]], "]"]], "6"]]], "+", RowBox[List["70", " ", SuperscriptBox[RowBox[List["Sec", "[", RowBox[List["c", " ", "z"]], "]"]], "8"]]], "+", RowBox[List["63", " ", SuperscriptBox[RowBox[List["Sec", "[", RowBox[List["c", " ", "z"]], "]"]], "10"]]]]], ")"]], " ", RowBox[List["Tan", "[", RowBox[List["c", " ", "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> <msup> <mi> sec </mi> <mn> 12 </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> <mrow> <mfrac> <mn> 1 </mn> <mrow> <mn> 693 </mn> <mo> ⁢ </mo> <mi> c </mi> </mrow> </mfrac> <mo> ⁢ </mo> <mrow> <mo> ( </mo> <mrow> <mrow> <mo> ( </mo> <mrow> <mrow> <mn> 63 </mn> <mo> ⁢ </mo> <mrow> <msup> <mi> sec </mi> <mn> 10 </mn> </msup> <mo> ( </mo> <mrow> <mi> c </mi> <mo> ⁢ </mo> <mi> z </mi> </mrow> <mo> ) </mo> </mrow> </mrow> <mo> + </mo> <mrow> <mn> 70 </mn> <mo> ⁢ </mo> <mrow> <msup> <mi> sec </mi> <mn> 8 </mn> </msup> <mo> ( </mo> <mrow> <mi> c </mi> <mo> ⁢ </mo> <mi> z </mi> </mrow> <mo> ) </mo> </mrow> </mrow> <mo> + </mo> <mrow> <mn> 80 </mn> <mo> ⁢ </mo> <mrow> <msup> <mi> sec </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> 96 </mn> <mo> ⁢ </mo> <mrow> <msup> <mi> sec </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> 128 </mn> <mo> ⁢ </mo> <mrow> <msup> <mi> sec </mi> <mn> 2 </mn> </msup> <mo> ( </mo> <mrow> <mi> c </mi> <mo> ⁢ </mo> <mi> z </mi> </mrow> <mo> ) </mo> </mrow> </mrow> <mo> + </mo> <mn> 256 </mn> </mrow> <mo> ) </mo> </mrow> <mo> ⁢ </mo> <mrow> <mi> tan </mi> <mo> ⁡ </mo> <mo> ( </mo> <mrow> <mi> c </mi> <mo> ⁢ </mo> <mi> z </mi> </mrow> <mo> ) </mo> </mrow> </mrow> <mo> ) </mo> </mrow> </mrow> </mrow> <annotation-xml encoding='MathML-Content'> <apply> <eq /> <apply> <int /> <bvar> <ci> z </ci> </bvar> <apply> <power /> <apply> <sec /> <apply> <times /> <ci> c </ci> <ci> z </ci> </apply> </apply> <cn type='integer'> 12 </cn> </apply> </apply> <apply> <times /> <apply> <times /> <cn type='integer'> 1 </cn> <apply> <power /> <apply> <times /> <cn type='integer'> 693 </cn> <ci> c </ci> </apply> <cn type='integer'> -1 </cn> </apply> </apply> <apply> <times /> <apply> <plus /> <apply> <times /> <cn type='integer'> 63 </cn> <apply> <power /> <apply> <sec /> <apply> <times /> <ci> c </ci> <ci> z </ci> </apply> </apply> <cn type='integer'> 10 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> 70 </cn> <apply> <power /> <apply> <sec /> <apply> <times /> <ci> c </ci> <ci> z </ci> </apply> </apply> <cn type='integer'> 8 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> 80 </cn> <apply> <power /> <apply> <sec /> <apply> <times /> <ci> c </ci> <ci> z </ci> </apply> </apply> <cn type='integer'> 6 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> 96 </cn> <apply> <power /> <apply> <sec /> <apply> <times /> <ci> c </ci> <ci> z </ci> </apply> </apply> <cn type='integer'> 4 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> 128 </cn> <apply> <power /> <apply> <sec /> <apply> <times /> <ci> c </ci> <ci> z </ci> </apply> </apply> <cn type='integer'> 2 </cn> </apply> </apply> <cn type='integer'> 256 </cn> </apply> <apply> <tan /> <apply> <times /> <ci> c </ci> <ci> z </ci> </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[SuperscriptBox[RowBox[List["Sec", "[", RowBox[List["c_", " ", "z_"]], "]"]], "12"], RowBox[List["\[DifferentialD]", "z_"]]]]]], "]"]], "\[RuleDelayed]", FractionBox[RowBox[List[RowBox[List["(", RowBox[List["256", "+", RowBox[List["128", " ", SuperscriptBox[RowBox[List["Sec", "[", RowBox[List["c", " ", "z"]], "]"]], "2"]]], "+", RowBox[List["96", " ", SuperscriptBox[RowBox[List["Sec", "[", RowBox[List["c", " ", "z"]], "]"]], "4"]]], "+", RowBox[List["80", " ", SuperscriptBox[RowBox[List["Sec", "[", RowBox[List["c", " ", "z"]], "]"]], "6"]]], "+", RowBox[List["70", " ", SuperscriptBox[RowBox[List["Sec", "[", RowBox[List["c", " ", "z"]], "]"]], "8"]]], "+", RowBox[List["63", " ", SuperscriptBox[RowBox[List["Sec", "[", RowBox[List["c", " ", "z"]], "]"]], "10"]]]]], ")"]], " ", RowBox[List["Tan", "[", RowBox[List["c", " ", "z"]], "]"]]]], RowBox[List["693", " ", "c"]]]]]]] |
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Date Added to functions.wolfram.com (modification date)
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