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Cosh




Mathematica Notation

Traditional Notation









Elementary Functions > Cosh[z] > Integration > Indefinite integration > Involving one direct function and elementary functions > Involving power function > Involving power > Involving zalpha-1and arguments a z





http://functions.wolfram.com/01.20.21.0041.01









  


  








Input Form





Integrate[z^7 Cosh[a z], z] == (1/a^8) (-7 (720 + 360 a^2 z^2 + 30 a^4 z^4 + a^6 z^6) Cosh[a z] + a z (5040 + 840 a^2 z^2 + 42 a^4 z^4 + a^6 z^6) Sinh[a z])








Standard Form





Cell[BoxData[RowBox[List[RowBox[List["\[Integral]", RowBox[List[SuperscriptBox["z", "7"], " ", RowBox[List["Cosh", "[", RowBox[List["a", " ", "z"]], "]"]], RowBox[List["\[DifferentialD]", "z"]]]]]], "\[Equal]", RowBox[List[FractionBox["1", SuperscriptBox["a", "8"]], RowBox[List["(", RowBox[List[RowBox[List[RowBox[List["-", "7"]], " ", RowBox[List["(", RowBox[List["720", "+", RowBox[List["360", " ", SuperscriptBox["a", "2"], " ", SuperscriptBox["z", "2"]]], "+", RowBox[List["30", " ", SuperscriptBox["a", "4"], " ", SuperscriptBox["z", "4"]]], "+", RowBox[List[SuperscriptBox["a", "6"], " ", SuperscriptBox["z", "6"]]]]], ")"]], " ", RowBox[List["Cosh", "[", RowBox[List["a", " ", "z"]], "]"]]]], "+", RowBox[List["a", " ", "z", " ", RowBox[List["(", RowBox[List["5040", "+", RowBox[List["840", " ", SuperscriptBox["a", "2"], " ", SuperscriptBox["z", "2"]]], "+", RowBox[List["42", " ", SuperscriptBox["a", "4"], " ", SuperscriptBox["z", "4"]]], "+", RowBox[List[SuperscriptBox["a", "6"], " ", SuperscriptBox["z", "6"]]]]], ")"]], " ", RowBox[List["Sinh", "[", RowBox[List["a", " ", "z"]], "]"]]]]]], ")"]]]]]]]]








MathML Form







<math xmlns='http://www.w3.org/1998/Math/MathML' mathematica:form='TraditionalForm' xmlns:mathematica='http://www.wolfram.com/XML/'> <semantics> <mrow> <mrow> <mo> &#8747; </mo> <mrow> <mrow> <msup> <mi> z </mi> <mn> 7 </mn> </msup> <mo> &#8290; </mo> <mrow> <mi> cosh </mi> <mo> &#8289; </mo> <mo> ( </mo> <mrow> <mi> a </mi> <mo> &#8290; </mo> <mi> z </mi> </mrow> <mo> ) </mo> </mrow> </mrow> <mo> &#8290; </mo> <mrow> <mo> &#8518; </mo> <mi> z </mi> </mrow> </mrow> </mrow> <mo> &#10869; </mo> <mrow> <mfrac> <mn> 1 </mn> <msup> <mi> a </mi> <mn> 8 </mn> </msup> </mfrac> <mo> &#8290; </mo> <mrow> <mo> ( </mo> <mrow> <mrow> <mi> a </mi> <mo> &#8290; </mo> <mi> z </mi> <mo> &#8290; </mo> <mrow> <mo> ( </mo> <mrow> <mrow> <msup> <mi> a </mi> <mn> 6 </mn> </msup> <mo> &#8290; </mo> <msup> <mi> z </mi> <mn> 6 </mn> </msup> </mrow> <mo> + </mo> <mrow> <mn> 42 </mn> <mo> &#8290; </mo> <msup> <mi> a </mi> <mn> 4 </mn> </msup> <mo> &#8290; </mo> <msup> <mi> z </mi> <mn> 4 </mn> </msup> </mrow> <mo> + </mo> <mrow> <mn> 840 </mn> <mo> &#8290; </mo> <msup> <mi> a </mi> <mn> 2 </mn> </msup> <mo> &#8290; </mo> <msup> <mi> z </mi> <mn> 2 </mn> </msup> </mrow> <mo> + </mo> <mn> 5040 </mn> </mrow> <mo> ) </mo> </mrow> <mo> &#8290; </mo> <mrow> <mi> sinh </mi> <mo> &#8289; </mo> <mo> ( </mo> <mrow> <mi> a </mi> <mo> &#8290; </mo> <mi> z </mi> </mrow> <mo> ) </mo> </mrow> </mrow> <mo> - </mo> <mrow> <mn> 7 </mn> <mo> &#8290; </mo> <mrow> <mo> ( </mo> <mrow> <mrow> <msup> <mi> a </mi> <mn> 6 </mn> </msup> <mo> &#8290; </mo> <msup> <mi> z </mi> <mn> 6 </mn> </msup> </mrow> <mo> + </mo> <mrow> <mn> 30 </mn> <mo> &#8290; </mo> <msup> <mi> a </mi> <mn> 4 </mn> </msup> <mo> &#8290; </mo> <msup> <mi> z </mi> <mn> 4 </mn> </msup> </mrow> <mo> + </mo> <mrow> <mn> 360 </mn> <mo> &#8290; </mo> <msup> <mi> a </mi> <mn> 2 </mn> </msup> <mo> &#8290; </mo> <msup> <mi> z </mi> <mn> 2 </mn> </msup> </mrow> <mo> + </mo> <mn> 720 </mn> </mrow> <mo> ) </mo> </mrow> <mo> &#8290; </mo> <mrow> <mi> cosh </mi> <mo> &#8289; </mo> <mo> ( </mo> <mrow> <mi> a </mi> <mo> &#8290; </mo> <mi> z </mi> </mrow> <mo> ) </mo> </mrow> </mrow> </mrow> <mo> ) </mo> </mrow> </mrow> </mrow> <annotation-xml encoding='MathML-Content'> <apply> <eq /> <apply> <int /> <bvar> <ci> z </ci> </bvar> <apply> <times /> <apply> <power /> <ci> z </ci> <cn type='integer'> 7 </cn> </apply> <apply> <cosh /> <apply> <times /> <ci> a </ci> <ci> z </ci> </apply> </apply> </apply> </apply> <apply> <times /> <apply> <times /> <cn type='integer'> 1 </cn> <apply> <power /> <apply> <power /> <ci> a </ci> <cn type='integer'> 8 </cn> </apply> <cn type='integer'> -1 </cn> </apply> </apply> <apply> <plus /> <apply> <times /> <ci> a </ci> <ci> z </ci> <apply> <plus /> <apply> <times /> <apply> <power /> <ci> a </ci> <cn type='integer'> 6 </cn> </apply> <apply> <power /> <ci> z </ci> <cn type='integer'> 6 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> 42 </cn> <apply> <power /> <ci> a </ci> <cn type='integer'> 4 </cn> </apply> <apply> <power /> <ci> z </ci> <cn type='integer'> 4 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> 840 </cn> <apply> <power /> <ci> a </ci> <cn type='integer'> 2 </cn> </apply> <apply> <power /> <ci> z </ci> <cn type='integer'> 2 </cn> </apply> </apply> <cn type='integer'> 5040 </cn> </apply> <apply> <sinh /> <apply> <times /> <ci> a </ci> <ci> z </ci> </apply> </apply> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <cn type='integer'> 7 </cn> <apply> <plus /> <apply> <times /> <apply> <power /> <ci> a </ci> <cn type='integer'> 6 </cn> </apply> <apply> <power /> <ci> z </ci> <cn type='integer'> 6 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> 30 </cn> <apply> <power /> <ci> a </ci> <cn type='integer'> 4 </cn> </apply> <apply> <power /> <ci> z </ci> <cn type='integer'> 4 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> 360 </cn> <apply> <power /> <ci> a </ci> <cn type='integer'> 2 </cn> </apply> <apply> <power /> <ci> z </ci> <cn type='integer'> 2 </cn> </apply> </apply> <cn type='integer'> 720 </cn> </apply> <apply> <cosh /> <apply> <times /> <ci> a </ci> <ci> z </ci> </apply> </apply> </apply> </apply> </apply> </apply> </apply> </annotation-xml> </semantics> </math>










Rule Form





Cell[BoxData[RowBox[List[RowBox[List["HoldPattern", "[", RowBox[List["\[Integral]", RowBox[List[RowBox[List[SuperscriptBox["z_", "7"], " ", RowBox[List["Cosh", "[", RowBox[List["a_", " ", "z_"]], "]"]]]], RowBox[List["\[DifferentialD]", "z_"]]]]]], "]"]], "\[RuleDelayed]", FractionBox[RowBox[List[RowBox[List[RowBox[List["-", "7"]], " ", RowBox[List["(", RowBox[List["720", "+", RowBox[List["360", " ", SuperscriptBox["a", "2"], " ", SuperscriptBox["z", "2"]]], "+", RowBox[List["30", " ", SuperscriptBox["a", "4"], " ", SuperscriptBox["z", "4"]]], "+", RowBox[List[SuperscriptBox["a", "6"], " ", SuperscriptBox["z", "6"]]]]], ")"]], " ", RowBox[List["Cosh", "[", RowBox[List["a", " ", "z"]], "]"]]]], "+", RowBox[List["a", " ", "z", " ", RowBox[List["(", RowBox[List["5040", "+", RowBox[List["840", " ", SuperscriptBox["a", "2"], " ", SuperscriptBox["z", "2"]]], "+", RowBox[List["42", " ", SuperscriptBox["a", "4"], " ", SuperscriptBox["z", "4"]]], "+", RowBox[List[SuperscriptBox["a", "6"], " ", SuperscriptBox["z", "6"]]]]], ")"]], " ", RowBox[List["Sinh", "[", RowBox[List["a", " ", "z"]], "]"]]]]]], SuperscriptBox["a", "8"]]]]]]


Date Added to functions.wolfram.com (modification date)





2002-12-18