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http://functions.wolfram.com/01.19.21.1460.01
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Integrate[Sinh[a z]^6, z] == (-60 a z + 45 Sinh[2 a z] - 9 Sinh[4 a z] +
Sinh[6 a z])/(192 a)
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Cell[BoxData[RowBox[List[RowBox[List["\[Integral]", RowBox[List[SuperscriptBox[RowBox[List["Sinh", "[", RowBox[List["a", " ", "z"]], "]"]], "6"], RowBox[List["\[DifferentialD]", "z"]]]]]], "\[Equal]", FractionBox[RowBox[List[RowBox[List[RowBox[List["-", "60"]], " ", "a", " ", "z"]], "+", RowBox[List["45", " ", RowBox[List["Sinh", "[", RowBox[List["2", " ", "a", " ", "z"]], "]"]]]], "-", RowBox[List["9", " ", RowBox[List["Sinh", "[", RowBox[List["4", " ", "a", " ", "z"]], "]"]]]], "+", RowBox[List["Sinh", "[", RowBox[List["6", " ", "a", " ", "z"]], "]"]]]], RowBox[List["192", " ", "a"]]]]]]]
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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> sinh </mi> <mn> 6 </mn> </msup> <mo> ( </mo> <mrow> <mi> a </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> <mrow> <mo> - </mo> <mn> 60 </mn> </mrow> <mo> ⁢ </mo> <mi> a </mi> <mo> ⁢ </mo> <mi> z </mi> </mrow> <mo> + </mo> <mrow> <mn> 45 </mn> <mo> ⁢ </mo> <mrow> <mi> sinh </mi> <mo> ⁡ </mo> <mo> ( </mo> <mrow> <mn> 2 </mn> <mo> ⁢ </mo> <mi> a </mi> <mo> ⁢ </mo> <mi> z </mi> </mrow> <mo> ) </mo> </mrow> </mrow> <mo> - </mo> <mrow> <mn> 9 </mn> <mo> ⁢ </mo> <mrow> <mi> sinh </mi> <mo> ⁡ </mo> <mo> ( </mo> <mrow> <mn> 4 </mn> <mo> ⁢ </mo> <mi> a </mi> <mo> ⁢ </mo> <mi> z </mi> </mrow> <mo> ) </mo> </mrow> </mrow> <mo> + </mo> <mrow> <mi> sinh </mi> <mo> ⁡ </mo> <mo> ( </mo> <mrow> <mn> 6 </mn> <mo> ⁢ </mo> <mi> a </mi> <mo> ⁢ </mo> <mi> z </mi> </mrow> <mo> ) </mo> </mrow> </mrow> <mrow> <mn> 192 </mn> <mo> ⁢ </mo> <mi> a </mi> </mrow> </mfrac> </mrow> <annotation-xml encoding='MathML-Content'> <apply> <eq /> <apply> <int /> <bvar> <ci> z </ci> </bvar> <apply> <power /> <apply> <sinh /> <apply> <times /> <ci> a </ci> <ci> z </ci> </apply> </apply> <cn type='integer'> 6 </cn> </apply> </apply> <apply> <times /> <apply> <plus /> <apply> <times /> <cn type='integer'> -60 </cn> <ci> a </ci> <ci> z </ci> </apply> <apply> <times /> <cn type='integer'> 45 </cn> <apply> <sinh /> <apply> <times /> <cn type='integer'> 2 </cn> <ci> a </ci> <ci> z </ci> </apply> </apply> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <cn type='integer'> 9 </cn> <apply> <sinh /> <apply> <times /> <cn type='integer'> 4 </cn> <ci> a </ci> <ci> z </ci> </apply> </apply> </apply> </apply> <apply> <sinh /> <apply> <times /> <cn type='integer'> 6 </cn> <ci> a </ci> <ci> z </ci> </apply> </apply> </apply> <apply> <power /> <apply> <times /> <cn type='integer'> 192 </cn> <ci> a </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["Sinh", "[", RowBox[List["a_", " ", "z_"]], "]"]], "6"], RowBox[List["\[DifferentialD]", "z_"]]]]]], "]"]], "\[RuleDelayed]", FractionBox[RowBox[List[RowBox[List[RowBox[List["-", "60"]], " ", "a", " ", "z"]], "+", RowBox[List["45", " ", RowBox[List["Sinh", "[", RowBox[List["2", " ", "a", " ", "z"]], "]"]]]], "-", RowBox[List["9", " ", RowBox[List["Sinh", "[", RowBox[List["4", " ", "a", " ", "z"]], "]"]]]], "+", RowBox[List["Sinh", "[", RowBox[List["6", " ", "a", " ", "z"]], "]"]]]], RowBox[List["192", " ", "a"]]]]]]] |
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Date Added to functions.wolfram.com (modification date)
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