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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+b





http://functions.wolfram.com/01.20.21.0071.01









  


  








Input Form





Integrate[Cosh[b + a z]/z^4, z] == (1/(6 z^3)) (-2 Cosh[b + a z] - a^2 z^2 Cosh[b + a z] + a^3 z^3 CoshIntegral[a z] Sinh[b] - a z Sinh[b + a z] + a^3 z^3 Cosh[b] SinhIntegral[a z])








Standard Form





Cell[BoxData[RowBox[List[RowBox[List["\[Integral]", RowBox[List[FractionBox[RowBox[List["Cosh", "[", RowBox[List["b", "+", RowBox[List["a", " ", "z"]]]], "]"]], SuperscriptBox["z", "4"]], RowBox[List["\[DifferentialD]", "z"]]]]]], "\[Equal]", RowBox[List[FractionBox["1", RowBox[List["6", " ", SuperscriptBox["z", "3"]]]], RowBox[List["(", RowBox[List[RowBox[List[RowBox[List["-", "2"]], " ", RowBox[List["Cosh", "[", RowBox[List["b", "+", RowBox[List["a", " ", "z"]]]], "]"]]]], "-", RowBox[List[SuperscriptBox["a", "2"], " ", SuperscriptBox["z", "2"], " ", RowBox[List["Cosh", "[", RowBox[List["b", "+", RowBox[List["a", " ", "z"]]]], "]"]]]], "+", RowBox[List[SuperscriptBox["a", "3"], " ", SuperscriptBox["z", "3"], " ", RowBox[List["CoshIntegral", "[", RowBox[List["a", " ", "z"]], "]"]], " ", RowBox[List["Sinh", "[", "b", "]"]]]], "-", RowBox[List["a", " ", "z", " ", RowBox[List["Sinh", "[", RowBox[List["b", "+", RowBox[List["a", " ", "z"]]]], "]"]]]], "+", RowBox[List[SuperscriptBox["a", "3"], " ", SuperscriptBox["z", "3"], " ", RowBox[List["Cosh", "[", "b", "]"]], " ", RowBox[List["SinhIntegral", "[", 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> <mfrac> <mrow> <mi> cosh </mi> <mo> &#8289; </mo> <mo> ( </mo> <mrow> <mi> b </mi> <mo> + </mo> <mrow> <mi> a </mi> <mo> &#8290; </mo> <mi> z </mi> </mrow> </mrow> <mo> ) </mo> </mrow> <msup> <mi> z </mi> <mn> 4 </mn> </msup> </mfrac> <mo> &#8290; </mo> <mrow> <mo> &#8518; </mo> <mi> z </mi> </mrow> </mrow> </mrow> <mo> &#10869; </mo> <mrow> <mfrac> <mn> 1 </mn> <mrow> <mn> 6 </mn> <mo> &#8290; </mo> <msup> <mi> z </mi> <mn> 3 </mn> </msup> </mrow> </mfrac> <mo> &#8290; </mo> <mrow> <mo> ( </mo> <mrow> <mrow> <msup> <mi> a </mi> <mn> 3 </mn> </msup> <mo> &#8290; </mo> <mrow> <mi> Chi </mi> <mo> &#8289; </mo> <mo> ( </mo> <mrow> <mi> a </mi> <mo> &#8290; </mo> <mi> z </mi> </mrow> <mo> ) </mo> </mrow> <mo> &#8290; </mo> <mrow> <mi> sinh </mi> <mo> &#8289; </mo> <mo> ( </mo> <mi> b </mi> <mo> ) </mo> </mrow> <mo> &#8290; </mo> <msup> <mi> z </mi> <mn> 3 </mn> </msup> </mrow> <mo> + </mo> <mrow> <msup> <mi> a </mi> <mn> 3 </mn> </msup> <mo> &#8290; </mo> <mrow> <mi> cosh </mi> <mo> &#8289; </mo> <mo> ( </mo> <mi> b </mi> <mo> ) </mo> </mrow> <mo> &#8290; </mo> <mrow> <mi> Shi </mi> <mo> &#8289; </mo> <mo> ( </mo> <mrow> <mi> a </mi> <mo> &#8290; </mo> <mi> z </mi> </mrow> <mo> ) </mo> </mrow> <mo> &#8290; </mo> <msup> <mi> z </mi> <mn> 3 </mn> </msup> </mrow> <mo> - </mo> <mrow> <msup> <mi> a </mi> <mn> 2 </mn> </msup> <mo> &#8290; </mo> <mrow> <mi> cosh </mi> <mo> &#8289; </mo> <mo> ( </mo> <mrow> <mi> b </mi> <mo> + </mo> <mrow> <mi> a </mi> <mo> &#8290; </mo> <mi> z </mi> </mrow> </mrow> <mo> ) </mo> </mrow> <mo> &#8290; </mo> <msup> <mi> z </mi> <mn> 2 </mn> </msup> </mrow> <mo> - </mo> <mrow> <mi> a </mi> <mo> &#8290; </mo> <mrow> <mi> sinh </mi> <mo> &#8289; </mo> <mo> ( </mo> <mrow> <mi> b </mi> <mo> + </mo> <mrow> <mi> a </mi> <mo> &#8290; </mo> <mi> z </mi> </mrow> </mrow> <mo> ) </mo> </mrow> <mo> &#8290; </mo> <mi> z </mi> </mrow> <mo> - </mo> <mrow> <mn> 2 </mn> <mo> &#8290; </mo> <mrow> <mi> cosh </mi> <mo> &#8289; </mo> <mo> ( </mo> <mrow> <mi> b </mi> <mo> + </mo> <mrow> <mi> a </mi> <mo> &#8290; </mo> <mi> z </mi> </mrow> </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> <cosh /> <apply> <plus /> <ci> b </ci> <apply> <times /> <ci> a </ci> <ci> z </ci> </apply> </apply> </apply> <apply> <power /> <apply> <power /> <ci> z </ci> <cn type='integer'> 4 </cn> </apply> <cn type='integer'> -1 </cn> </apply> </apply> </apply> <apply> <times /> <apply> <times /> <cn type='integer'> 1 </cn> <apply> <power /> <apply> <times /> <cn type='integer'> 6 </cn> <apply> <power /> <ci> z </ci> <cn type='integer'> 3 </cn> </apply> </apply> <cn type='integer'> -1 </cn> </apply> </apply> <apply> <plus /> <apply> <times /> <apply> <power /> <ci> a </ci> <cn type='integer'> 3 </cn> </apply> <apply> <ci> CoshIntegral </ci> <apply> <times /> <ci> a </ci> <ci> z </ci> </apply> </apply> <apply> <sinh /> <ci> b </ci> </apply> <apply> <power /> <ci> z </ci> <cn type='integer'> 3 </cn> </apply> </apply> <apply> <times /> <apply> <power /> <ci> a </ci> <cn type='integer'> 3 </cn> </apply> <apply> <cosh /> <ci> b </ci> </apply> <apply> <ci> SinhIntegral </ci> <apply> <times /> <ci> a </ci> <ci> z </ci> </apply> </apply> <apply> <power /> <ci> z </ci> <cn type='integer'> 3 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <apply> <power /> <ci> a </ci> <cn type='integer'> 2 </cn> </apply> <apply> <cosh /> <apply> <plus /> <ci> b </ci> <apply> <times /> <ci> a </ci> <ci> z </ci> </apply> </apply> </apply> <apply> <power /> <ci> z </ci> <cn type='integer'> 2 </cn> </apply> </apply> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <ci> a </ci> <apply> <sinh /> <apply> <plus /> <ci> b </ci> <apply> <times /> <ci> a </ci> <ci> z </ci> </apply> </apply> </apply> <ci> z </ci> </apply> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <cn type='integer'> 2 </cn> <apply> <cosh /> <apply> <plus /> <ci> b </ci> <apply> <times /> <ci> a </ci> <ci> z </ci> </apply> </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[FractionBox[RowBox[List["Cosh", "[", RowBox[List["b_", "+", RowBox[List["a_", " ", "z_"]]]], "]"]], SuperscriptBox["z_", "4"]], RowBox[List["\[DifferentialD]", "z_"]]]]]], "]"]], "\[RuleDelayed]", FractionBox[RowBox[List[RowBox[List[RowBox[List["-", "2"]], " ", RowBox[List["Cosh", "[", RowBox[List["b", "+", RowBox[List["a", " ", "z"]]]], "]"]]]], "-", RowBox[List[SuperscriptBox["a", "2"], " ", SuperscriptBox["z", "2"], " ", RowBox[List["Cosh", "[", RowBox[List["b", "+", RowBox[List["a", " ", "z"]]]], "]"]]]], "+", RowBox[List[SuperscriptBox["a", "3"], " ", SuperscriptBox["z", "3"], " ", RowBox[List["CoshIntegral", "[", RowBox[List["a", " ", "z"]], "]"]], " ", RowBox[List["Sinh", "[", "b", "]"]]]], "-", RowBox[List["a", " ", "z", " ", RowBox[List["Sinh", "[", RowBox[List["b", "+", RowBox[List["a", " ", "z"]]]], "]"]]]], "+", RowBox[List[SuperscriptBox["a", "3"], " ", SuperscriptBox["z", "3"], " ", RowBox[List["Cosh", "[", "b", "]"]], " ", RowBox[List["SinhIntegral", "[", RowBox[List["a", " ", "z"]], "]"]]]]]], RowBox[List["6", " ", SuperscriptBox["z", "3"]]]]]]]]


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





2002-12-18