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CoshIntegral






Mathematica Notation

Traditional Notation









Gamma, Beta, Erf > CoshIntegral[z] > Integration > Indefinite integration > Involving functions of the direct function and elementary functions > Involving elementary functions of the direct function and elementary functions > Involving powers of the direct function and a power function





http://functions.wolfram.com/06.40.21.0052.01









  


  










Input Form





Integrate[z^2 CoshIntegral[a z]^2, z] == (1/(12 a^3)) (-8 a z + 2 a z Cosh[2 a z] + 4 a^3 z^3 CoshIntegral[a z]^2 - 8 CoshIntegral[a z] (-2 a z Cosh[a z] + (2 + a^2 z^2) Sinh[a z]) - 5 Sinh[2 a z] + 8 SinhIntegral[2 a z])










Standard Form





Cell[BoxData[RowBox[List[RowBox[List["\[Integral]", RowBox[List[SuperscriptBox["z", "2"], " ", SuperscriptBox[RowBox[List["CoshIntegral", "[", RowBox[List["a", " ", "z"]], "]"]], "2"], RowBox[List["\[DifferentialD]", "z"]]]]]], "\[Equal]", RowBox[List[FractionBox["1", RowBox[List["12", " ", SuperscriptBox["a", "3"]]]], RowBox[List["(", RowBox[List[RowBox[List[RowBox[List["-", "8"]], " ", "a", " ", "z"]], "+", RowBox[List["2", " ", "a", " ", "z", " ", RowBox[List["Cosh", "[", RowBox[List["2", " ", "a", " ", "z"]], "]"]]]], "+", RowBox[List["4", " ", SuperscriptBox["a", "3"], " ", SuperscriptBox["z", "3"], " ", SuperscriptBox[RowBox[List["CoshIntegral", "[", RowBox[List["a", " ", "z"]], "]"]], "2"]]], "-", RowBox[List["8", " ", RowBox[List["CoshIntegral", "[", RowBox[List["a", " ", "z"]], "]"]], " ", RowBox[List["(", RowBox[List[RowBox[List[RowBox[List["-", "2"]], " ", "a", " ", "z", " ", RowBox[List["Cosh", "[", RowBox[List["a", " ", "z"]], "]"]]]], "+", RowBox[List[RowBox[List["(", RowBox[List["2", "+", RowBox[List[SuperscriptBox["a", "2"], " ", SuperscriptBox["z", "2"]]]]], ")"]], " ", RowBox[List["Sinh", "[", RowBox[List["a", " ", "z"]], "]"]]]]]], ")"]]]], "-", RowBox[List["5", " ", RowBox[List["Sinh", "[", RowBox[List["2", " ", "a", " ", "z"]], "]"]]]], "+", RowBox[List["8", " ", RowBox[List["SinhIntegral", "[", RowBox[List["2", " ", "a", " ", "z"]], "]"]]]]]], ")"]]]]]]]]










MathML Form







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</mo> <mi> a </mi> <mo> &#8290; </mo> <mi> z </mi> </mrow> <mo> + </mo> <mrow> <mn> 2 </mn> <mo> &#8290; </mo> <mi> a </mi> <mo> &#8290; </mo> <mrow> <mi> cosh </mi> <mo> &#8289; </mo> <mo> ( </mo> <mrow> <mn> 2 </mn> <mo> &#8290; </mo> <mi> a </mi> <mo> &#8290; </mo> <mi> z </mi> </mrow> <mo> ) </mo> </mrow> <mo> &#8290; </mo> <mi> z </mi> </mrow> <mo> - </mo> <mrow> <mn> 8 </mn> <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> <mo> ( </mo> <mrow> <mrow> <mrow> <mo> ( </mo> <mrow> <mrow> <msup> <mi> a </mi> <mn> 2 </mn> </msup> <mo> &#8290; </mo> <msup> <mi> z </mi> <mn> 2 </mn> </msup> </mrow> <mo> + </mo> <mn> 2 </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> 2 </mn> <mo> &#8290; </mo> <mi> a </mi> <mo> &#8290; </mo> <mi> z </mi> <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> <mo> - </mo> <mrow> <mn> 5 </mn> <mo> &#8290; </mo> <mrow> <mi> sinh </mi> <mo> &#8289; </mo> <mo> ( </mo> <mrow> <mn> 2 </mn> <mo> &#8290; </mo> <mi> a </mi> <mo> &#8290; </mo> <mi> z </mi> </mrow> <mo> ) </mo> </mrow> </mrow> <mo> + </mo> <mrow> <mn> 8 </mn> <mo> &#8290; </mo> <mrow> <mi> Shi </mi> <mo> &#8289; </mo> <mo> ( </mo> <mrow> <mn> 2 </mn> <mo> &#8290; </mo> <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'> 2 </cn> </apply> <apply> <power /> <apply> <ci> CoshIntegral </ci> <apply> <times /> <ci> a </ci> <ci> z </ci> </apply> </apply> <cn type='integer'> 2 </cn> </apply> </apply> </apply> <apply> <times /> <apply> <times /> <cn type='integer'> 1 </cn> <apply> <power /> <apply> <times /> <cn type='integer'> 12 </cn> <apply> <power /> <ci> a </ci> <cn type='integer'> 3 </cn> </apply> </apply> <cn type='integer'> -1 </cn> </apply> </apply> <apply> <plus /> <apply> <times /> <cn type='integer'> 4 </cn> <apply> <power /> <ci> a </ci> <cn type='integer'> 3 </cn> </apply> <apply> <power /> <apply> <ci> CoshIntegral </ci> <apply> <times /> <ci> a </ci> <ci> z </ci> </apply> </apply> <cn type='integer'> 2 </cn> </apply> <apply> <power /> <ci> z </ci> <cn type='integer'> 3 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <cn type='integer'> 8 </cn> <ci> a </ci> <ci> z </ci> </apply> </apply> <apply> <times /> <cn type='integer'> 2 </cn> <ci> a </ci> <apply> <cosh /> <apply> <times /> <cn type='integer'> 2 </cn> <ci> a </ci> <ci> z </ci> </apply> </apply> <ci> z </ci> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <cn type='integer'> 8 </cn> <apply> <ci> CoshIntegral </ci> <apply> <times /> <ci> a </ci> <ci> z </ci> </apply> </apply> <apply> <plus /> <apply> <times /> <apply> <plus /> <apply> <times /> <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'> 2 </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'> 2 </cn> <ci> a </ci> <ci> z </ci> <apply> <cosh /> <apply> <times /> <ci> a </ci> <ci> z </ci> </apply> </apply> </apply> </apply> </apply> </apply> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <cn type='integer'> 5 </cn> <apply> <sinh /> <apply> <times /> <cn type='integer'> 2 </cn> <ci> a </ci> <ci> z </ci> </apply> </apply> </apply> </apply> <apply> <times /> <cn type='integer'> 8 </cn> <apply> <ci> SinhIntegral </ci> <apply> <times /> <cn type='integer'> 2 </cn> <ci> a </ci> <ci> z </ci> </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_", "2"], " ", SuperscriptBox[RowBox[List["CoshIntegral", "[", RowBox[List["a_", " ", "z_"]], "]"]], "2"]]], RowBox[List["\[DifferentialD]", "z_"]]]]]], "]"]], "\[RuleDelayed]", FractionBox[RowBox[List[RowBox[List[RowBox[List["-", "8"]], " ", "a", " ", "z"]], "+", RowBox[List["2", " ", "a", " ", "z", " ", RowBox[List["Cosh", "[", RowBox[List["2", " ", "a", " ", "z"]], "]"]]]], "+", RowBox[List["4", " ", SuperscriptBox["a", "3"], " ", SuperscriptBox["z", "3"], " ", SuperscriptBox[RowBox[List["CoshIntegral", "[", RowBox[List["a", " ", "z"]], "]"]], "2"]]], "-", RowBox[List["8", " ", RowBox[List["CoshIntegral", "[", RowBox[List["a", " ", "z"]], "]"]], " ", RowBox[List["(", RowBox[List[RowBox[List[RowBox[List["-", "2"]], " ", "a", " ", "z", " ", RowBox[List["Cosh", "[", RowBox[List["a", " ", "z"]], "]"]]]], "+", RowBox[List[RowBox[List["(", RowBox[List["2", "+", RowBox[List[SuperscriptBox["a", "2"], " ", SuperscriptBox["z", "2"]]]]], ")"]], " ", RowBox[List["Sinh", "[", RowBox[List["a", " ", "z"]], "]"]]]]]], ")"]]]], "-", RowBox[List["5", " ", RowBox[List["Sinh", "[", RowBox[List["2", " ", "a", " ", "z"]], "]"]]]], "+", RowBox[List["8", " ", RowBox[List["SinhIntegral", "[", RowBox[List["2", " ", "a", " ", "z"]], "]"]]]]]], RowBox[List["12", " ", SuperscriptBox["a", "3"]]]]]]]]










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





2001-10-29





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