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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 zr+b





http://functions.wolfram.com/01.20.21.0129.01









  


  








Input Form





Integrate[z^2 Cosh[a Sqrt[z] + b], z] == (1/a^6) (2 (-5 (24 + 12 a^2 z + a^4 z^2) Cosh[b + a Sqrt[z]] + a Sqrt[z] (120 + 20 a^2 z + a^4 z^2) Sinh[b + a Sqrt[z]]))








Standard Form





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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> 2 </mn> </msup> <mo> &#8290; </mo> <mrow> <mi> cosh </mi> <mo> &#8289; </mo> <mo> ( </mo> <mrow> <mrow> <msqrt> <mi> z </mi> </msqrt> <mo> &#8290; </mo> <mi> a </mi> </mrow> <mo> + </mo> <mi> b </mi> </mrow> <mo> ) </mo> </mrow> </mrow> <mo> &#8290; </mo> <mrow> <mo> &#8518; </mo> <mi> z </mi> </mrow> </mrow> </mrow> <mo> &#10869; </mo> <mfrac> <mrow> <mn> 2 </mn> <mo> &#8290; </mo> <mrow> <mo> ( </mo> <mrow> <mrow> <mi> a </mi> <mo> &#8290; </mo> <msqrt> <mi> z </mi> </msqrt> <mo> &#8290; </mo> <mrow> <mo> ( </mo> <mrow> <mrow> <msup> <mi> z </mi> <mn> 2 </mn> </msup> <mo> &#8290; </mo> <msup> <mi> a </mi> <mn> 4 </mn> </msup> </mrow> <mo> + </mo> <mrow> <mn> 20 </mn> <mo> &#8290; </mo> <mi> z </mi> <mo> &#8290; </mo> <msup> <mi> a </mi> <mn> 2 </mn> </msup> </mrow> <mo> + </mo> <mn> 120 </mn> </mrow> <mo> ) </mo> </mrow> <mo> &#8290; </mo> <mrow> <mi> sinh </mi> <mo> &#8289; </mo> <mo> ( </mo> <mrow> <mrow> <msqrt> <mi> z </mi> </msqrt> <mo> &#8290; </mo> <mi> a </mi> </mrow> <mo> + </mo> <mi> b </mi> </mrow> <mo> ) </mo> </mrow> </mrow> <mo> - </mo> <mrow> <mn> 5 </mn> <mo> &#8290; </mo> <mrow> <mo> ( </mo> <mrow> <mrow> <msup> <mi> z </mi> <mn> 2 </mn> </msup> <mo> &#8290; </mo> <msup> <mi> a </mi> <mn> 4 </mn> </msup> </mrow> <mo> + </mo> <mrow> <mn> 12 </mn> <mo> &#8290; </mo> <mi> z </mi> <mo> &#8290; </mo> <msup> <mi> a </mi> <mn> 2 </mn> </msup> </mrow> <mo> + </mo> <mn> 24 </mn> </mrow> <mo> ) </mo> </mrow> <mo> &#8290; </mo> <mrow> <mi> cosh </mi> <mo> &#8289; </mo> <mo> ( </mo> <mrow> <mrow> <msqrt> <mi> z </mi> </msqrt> <mo> &#8290; </mo> <mi> a </mi> </mrow> <mo> + </mo> <mi> b </mi> </mrow> <mo> ) </mo> </mrow> </mrow> </mrow> <mo> ) </mo> </mrow> </mrow> <msup> <mi> a </mi> <mn> 6 </mn> </msup> </mfrac> </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'> 2 </cn> </apply> <apply> <cosh /> <apply> <plus /> <apply> <times /> <apply> <power /> <ci> z </ci> <cn type='rational'> 1 <sep /> 2 </cn> </apply> <ci> a </ci> </apply> <ci> b </ci> </apply> </apply> </apply> </apply> <apply> <times /> <cn type='integer'> 2 </cn> <apply> <plus /> <apply> <times /> <ci> a </ci> <apply> <power /> <ci> z </ci> <cn type='rational'> 1 <sep /> 2 </cn> </apply> <apply> <plus /> <apply> <times /> <apply> <power /> <ci> z </ci> <cn type='integer'> 2 </cn> </apply> <apply> <power /> <ci> a </ci> <cn type='integer'> 4 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> 20 </cn> <ci> z </ci> <apply> <power /> <ci> a </ci> <cn type='integer'> 2 </cn> </apply> </apply> <cn type='integer'> 120 </cn> </apply> <apply> <sinh /> <apply> <plus /> <apply> <times /> <apply> <power /> <ci> z </ci> <cn type='rational'> 1 <sep /> 2 </cn> </apply> <ci> a </ci> </apply> <ci> b </ci> </apply> </apply> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <cn type='integer'> 5 </cn> <apply> <plus /> <apply> <times /> <apply> <power /> <ci> z </ci> <cn type='integer'> 2 </cn> </apply> <apply> <power /> <ci> a </ci> <cn type='integer'> 4 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> 12 </cn> <ci> z </ci> <apply> <power /> <ci> a </ci> <cn type='integer'> 2 </cn> </apply> </apply> <cn type='integer'> 24 </cn> </apply> <apply> <cosh /> <apply> <plus /> <apply> <times /> <apply> <power /> <ci> z </ci> <cn type='rational'> 1 <sep /> 2 </cn> </apply> <ci> a </ci> </apply> <ci> b </ci> </apply> </apply> </apply> </apply> </apply> <apply> <power /> <apply> <power /> <ci> a </ci> <cn type='integer'> 6 </cn> </apply> <cn type='integer'> -1 </cn> </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_", "2"], " ", RowBox[List["Cosh", "[", RowBox[List[RowBox[List["a_", " ", SqrtBox["z_"]]], "+", "b_"]], "]"]]]], RowBox[List["\[DifferentialD]", "z_"]]]]]], "]"]], "\[RuleDelayed]", FractionBox[RowBox[List["2", " ", RowBox[List["(", RowBox[List[RowBox[List[RowBox[List["-", "5"]], " ", RowBox[List["(", RowBox[List["24", "+", RowBox[List["12", " ", SuperscriptBox["a", "2"], " ", "z"]], "+", RowBox[List[SuperscriptBox["a", "4"], " ", SuperscriptBox["z", "2"]]]]], ")"]], " ", RowBox[List["Cosh", "[", RowBox[List["b", "+", RowBox[List["a", " ", SqrtBox["z"]]]]], "]"]]]], "+", RowBox[List["a", " ", SqrtBox["z"], " ", RowBox[List["(", RowBox[List["120", "+", RowBox[List["20", " ", SuperscriptBox["a", "2"], " ", "z"]], "+", RowBox[List[SuperscriptBox["a", "4"], " ", SuperscriptBox["z", "2"]]]]], ")"]], " ", RowBox[List["Sinh", "[", RowBox[List["b", "+", RowBox[List["a", " ", SqrtBox["z"]]]]], "]"]]]]]], ")"]]]], SuperscriptBox["a", "6"]]]]]]


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





2002-12-18