Wolfram Researchfunctions.wolfram.comOther Wolfram Sites
Search Site
Function CategoriesGraphics GalleryNotationsGeneral IdentitiesAbout This Site Email Comments

View Related Information In
The Documentation Center
MathWorld

Download All Formulas For This Function
Mathematica Notebook
PDF File

Download All Introductions For This Function
Mathematica Notebook
PDF File

 

Developed with Mathematica -- Download a Free Trial Version
 











CosIntegral




Mathematica Notation

Traditional Notation









Gamma, Beta, Erf > CosIntegral[z] > Integration > Indefinite integration > Involving one direct function and elementary functions > Involving trigonometric functions and a power function > Involving sin and power





http://functions.wolfram.com/06.38.21.0028.01









  


  








Input Form





Integrate[z^3 Sin[b z] CosIntegral[a z], z] == (1/(2 b^4)) (3 I (-ExpIntegralEi[(-I) (a - b) z] + ExpIntegralEi[I (a - b) z] + ExpIntegralEi[(-I) (a + b) z] - ExpIntegralEi[I (a + b) z]) + (1/((a - b)^3 (a + b)^3)) (2 a b Sin[a z] ((b^4 (-18 + b^2 z^2) - 2 a^2 b^2 (-8 + b^2 z^2) + a^4 (-6 + b^2 z^2)) Cos[b z] + b (-3 a^4 + 10 a^2 b^2 - 7 b^4) z Sin[b z])) - 2 CosIntegral[a z] (b z (-6 + b^2 z^2) Cos[b z] - 3 (-2 + b^2 z^2) Sin[b z]) + (1/((-a + b)^3 (a + b)^3)) (2 b^2 Cos[a z] (b (a^4 - 6 a^2 b^2 + 5 b^4) z Cos[b z] + (b^4 (-11 + b^2 z^2) + a^4 (-3 + b^2 z^2) + a^2 (6 b^2 - 2 b^4 z^2)) Sin[b z])))








Standard Form





Cell[BoxData[RowBox[List[RowBox[List["\[Integral]", RowBox[List[SuperscriptBox["z", "3"], " ", RowBox[List["Sin", "[", RowBox[List["b", " ", "z"]], "]"]], RowBox[List["CosIntegral", "[", RowBox[List["a", " ", "z"]], "]"]], RowBox[List["\[DifferentialD]", "z"]]]]]], "\[Equal]", RowBox[List[FractionBox["1", RowBox[List["2", " ", SuperscriptBox["b", "4"]]]], RowBox[List["(", RowBox[List[RowBox[List["3", " ", "\[ImaginaryI]", " ", RowBox[List["(", RowBox[List[RowBox[List["-", RowBox[List["ExpIntegralEi", "[", RowBox[List[RowBox[List["-", "\[ImaginaryI]"]], " ", RowBox[List["(", RowBox[List["a", "-", "b"]], ")"]], " ", "z"]], "]"]]]], "+", RowBox[List["ExpIntegralEi", "[", RowBox[List["\[ImaginaryI]", " ", RowBox[List["(", RowBox[List["a", "-", "b"]], ")"]], " ", "z"]], "]"]], "+", RowBox[List["ExpIntegralEi", "[", RowBox[List[RowBox[List["-", "\[ImaginaryI]"]], " ", RowBox[List["(", RowBox[List["a", "+", "b"]], ")"]], " ", "z"]], "]"]], "-", RowBox[List["ExpIntegralEi", "[", RowBox[List["\[ImaginaryI]", " ", RowBox[List["(", RowBox[List["a", "+", "b"]], ")"]], " ", "z"]], "]"]]]], ")"]]]], "+", RowBox[List[FractionBox["1", RowBox[List[SuperscriptBox[RowBox[List["(", RowBox[List["a", "-", "b"]], ")"]], "3"], " ", SuperscriptBox[RowBox[List["(", RowBox[List["a", "+", "b"]], ")"]], "3"]]]], RowBox[List["(", RowBox[List["2", " ", "a", " ", "b", " ", RowBox[List["Sin", "[", RowBox[List["a", " ", "z"]], "]"]], " ", RowBox[List["(", RowBox[List[RowBox[List[RowBox[List["(", RowBox[List[RowBox[List[SuperscriptBox["b", "4"], " ", RowBox[List["(", RowBox[List[RowBox[List["-", "18"]], "+", RowBox[List[SuperscriptBox["b", "2"], " ", SuperscriptBox["z", "2"]]]]], ")"]]]], "-", RowBox[List["2", " ", SuperscriptBox["a", "2"], " ", SuperscriptBox["b", "2"], " ", RowBox[List["(", RowBox[List[RowBox[List["-", "8"]], "+", RowBox[List[SuperscriptBox["b", "2"], " ", SuperscriptBox["z", "2"]]]]], ")"]]]], "+", RowBox[List[SuperscriptBox["a", "4"], " ", RowBox[List["(", RowBox[List[RowBox[List["-", "6"]], "+", RowBox[List[SuperscriptBox["b", "2"], " ", SuperscriptBox["z", "2"]]]]], ")"]]]]]], ")"]], " ", RowBox[List["Cos", "[", RowBox[List["b", " ", "z"]], "]"]]]], "+", RowBox[List["b", " ", RowBox[List["(", RowBox[List[RowBox[List[RowBox[List["-", "3"]], " ", SuperscriptBox["a", "4"]]], "+", RowBox[List["10", " ", SuperscriptBox["a", "2"], " ", SuperscriptBox["b", "2"]]], "-", RowBox[List["7", " ", SuperscriptBox["b", "4"]]]]], ")"]], " ", "z", " ", RowBox[List["Sin", "[", RowBox[List["b", " ", "z"]], "]"]]]]]], ")"]]]], ")"]]]], "-", RowBox[List["2", " ", RowBox[List["CosIntegral", "[", RowBox[List["a", " ", "z"]], "]"]], " ", RowBox[List["(", RowBox[List[RowBox[List["b", " ", "z", " ", RowBox[List["(", RowBox[List[RowBox[List["-", "6"]], "+", RowBox[List[SuperscriptBox["b", "2"], " ", SuperscriptBox["z", "2"]]]]], ")"]], " ", RowBox[List["Cos", "[", RowBox[List["b", " ", "z"]], "]"]]]], "-", RowBox[List["3", " ", RowBox[List["(", RowBox[List[RowBox[List["-", "2"]], "+", RowBox[List[SuperscriptBox["b", "2"], " ", SuperscriptBox["z", "2"]]]]], ")"]], " ", RowBox[List["Sin", "[", RowBox[List["b", " ", "z"]], "]"]]]]]], ")"]]]], "+", RowBox[List[FractionBox["1", RowBox[List[SuperscriptBox[RowBox[List["(", RowBox[List[RowBox[List["-", "a"]], "+", "b"]], ")"]], "3"], " ", SuperscriptBox[RowBox[List["(", RowBox[List["a", "+", "b"]], ")"]], "3"]]]], RowBox[List["(", RowBox[List["2", " ", SuperscriptBox["b", "2"], " ", RowBox[List["Cos", "[", RowBox[List["a", " ", "z"]], "]"]], " ", RowBox[List["(", RowBox[List[RowBox[List["b", " ", RowBox[List["(", RowBox[List[SuperscriptBox["a", "4"], "-", RowBox[List["6", " ", SuperscriptBox["a", "2"], " ", SuperscriptBox["b", "2"]]], "+", RowBox[List["5", " ", SuperscriptBox["b", "4"]]]]], ")"]], " ", "z", " ", RowBox[List["Cos", "[", RowBox[List["b", " ", "z"]], "]"]]]], "+", RowBox[List[RowBox[List["(", RowBox[List[RowBox[List[SuperscriptBox["b", "4"], " ", RowBox[List["(", RowBox[List[RowBox[List["-", "11"]], "+", RowBox[List[SuperscriptBox["b", "2"], " ", SuperscriptBox["z", "2"]]]]], ")"]]]], "+", RowBox[List[SuperscriptBox["a", "4"], " ", RowBox[List["(", RowBox[List[RowBox[List["-", "3"]], "+", RowBox[List[SuperscriptBox["b", "2"], " ", SuperscriptBox["z", "2"]]]]], ")"]]]], "+", RowBox[List[SuperscriptBox["a", "2"], " ", RowBox[List["(", RowBox[List[RowBox[List["6", " ", SuperscriptBox["b", "2"]]], "-", RowBox[List["2", " ", SuperscriptBox["b", "4"], " ", SuperscriptBox["z", "2"]]]]], ")"]]]]]], ")"]], " ", RowBox[List["Sin", "[", RowBox[List["b", " ", "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> 3 </mn> </msup> <mo> &#8290; </mo> <mrow> <mi> sin </mi> <mo> &#8289; </mo> <mo> ( </mo> <mrow> <mi> b </mi> <mo> &#8290; </mo> <mi> z </mi> </mrow> <mo> ) </mo> </mrow> <mo> &#8290; </mo> <mrow> <mi> Ci </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> <mrow> <mn> 2 </mn> <mo> &#8290; </mo> <msup> <mi> b </mi> <mn> 4 </mn> </msup> </mrow> </mfrac> <mo> &#8290; </mo> <mrow> <mo> ( </mo> <mrow> <mrow> <mn> 3 </mn> <mo> &#8290; </mo> <mi> &#8520; </mi> <mo> &#8290; </mo> <mrow> <mo> ( </mo> <mrow> <mrow> <mo> - </mo> <mrow> <mi> Ei </mi> <mo> &#8289; </mo> <mo> ( </mo> <mrow> <mrow> <mo> - </mo> <mi> &#8520; </mi> </mrow> <mo> &#8290; </mo> <mrow> <mo> ( </mo> <mrow> <mi> a </mi> <mo> - </mo> <mi> b </mi> </mrow> <mo> ) </mo> </mrow> <mo> &#8290; </mo> <mi> z </mi> </mrow> <mo> ) </mo> </mrow> </mrow> <mo> + </mo> <mrow> <mi> Ei </mi> <mo> &#8289; </mo> <mo> ( </mo> <mrow> <mi> &#8520; </mi> <mo> &#8290; </mo> <mrow> <mo> ( </mo> <mrow> <mi> a </mi> <mo> - </mo> <mi> b </mi> </mrow> <mo> ) </mo> </mrow> <mo> &#8290; </mo> <mi> z </mi> </mrow> <mo> ) </mo> </mrow> <mo> + </mo> <mrow> <mi> Ei </mi> <mo> &#8289; </mo> <mo> ( </mo> <mrow> <mrow> <mo> - </mo> <mi> &#8520; </mi> </mrow> <mo> &#8290; </mo> <mrow> <mo> ( </mo> <mrow> <mi> a </mi> <mo> + </mo> <mi> b </mi> </mrow> <mo> ) </mo> </mrow> <mo> &#8290; </mo> <mi> z </mi> </mrow> <mo> ) </mo> </mrow> <mo> - </mo> <mrow> <mi> Ei </mi> <mo> &#8289; </mo> <mo> ( </mo> <mrow> <mi> &#8520; </mi> <mo> &#8290; </mo> <mrow> <mo> ( </mo> <mrow> <mi> a </mi> <mo> + </mo> <mi> b </mi> </mrow> <mo> ) </mo> </mrow> <mo> &#8290; </mo> <mi> z </mi> </mrow> <mo> ) </mo> </mrow> </mrow> <mo> ) </mo> </mrow> </mrow> <mo> + </mo> <mrow> <mfrac> <mn> 1 </mn> <mrow> <msup> <mrow> <mo> ( </mo> <mrow> <mi> a </mi> <mo> - </mo> <mi> b </mi> </mrow> <mo> ) </mo> </mrow> <mn> 3 </mn> </msup> <mo> &#8290; </mo> <msup> <mrow> <mo> ( </mo> <mrow> <mi> a </mi> <mo> + </mo> <mi> b </mi> </mrow> <mo> ) </mo> </mrow> <mn> 3 </mn> </msup> </mrow> </mfrac> <mo> &#8290; </mo> <mrow> <mo> ( </mo> <mrow> <mn> 2 </mn> <mo> &#8290; </mo> <mi> a </mi> <mo> &#8290; </mo> <mi> b </mi> <mo> &#8290; </mo> <mrow> <mi> sin </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> <mrow> <mo> ( </mo> <mrow> <mrow> <msup> <mi> b </mi> <mn> 2 </mn> </msup> <mo> &#8290; </mo> <msup> <mi> z </mi> <mn> 2 </mn> </msup> </mrow> <mo> - </mo> <mn> 6 </mn> </mrow> <mo> ) </mo> </mrow> <mo> &#8290; </mo> <msup> <mi> a </mi> <mn> 4 </mn> </msup> </mrow> <mo> - </mo> <mrow> <mn> 2 </mn> <mo> &#8290; </mo> <msup> <mi> b </mi> <mn> 2 </mn> </msup> <mo> &#8290; </mo> <mrow> <mo> ( </mo> <mrow> <mrow> <msup> <mi> b </mi> <mn> 2 </mn> </msup> <mo> &#8290; </mo> <msup> <mi> z </mi> <mn> 2 </mn> </msup> </mrow> <mo> - </mo> <mn> 8 </mn> </mrow> <mo> ) </mo> </mrow> <mo> &#8290; </mo> <msup> <mi> a </mi> <mn> 2 </mn> </msup> </mrow> <mo> + </mo> <mrow> <msup> <mi> b </mi> <mn> 4 </mn> </msup> <mo> &#8290; </mo> <mrow> <mo> ( </mo> <mrow> <mrow> <msup> <mi> b </mi> <mn> 2 </mn> </msup> <mo> &#8290; </mo> <msup> <mi> z </mi> <mn> 2 </mn> </msup> </mrow> <mo> - </mo> <mn> 18 </mn> </mrow> <mo> ) </mo> </mrow> </mrow> </mrow> <mo> ) </mo> </mrow> <mo> &#8290; </mo> <mrow> <mi> cos </mi> <mo> &#8289; </mo> <mo> ( </mo> <mrow> <mi> b </mi> <mo> &#8290; </mo> <mi> z </mi> </mrow> <mo> ) </mo> </mrow> </mrow> <mo> + </mo> <mrow> <mi> b </mi> <mo> &#8290; </mo> <mrow> <mo> ( </mo> <mrow> <mrow> <mrow> <mo> - </mo> <mn> 3 </mn> </mrow> <mo> &#8290; </mo> <msup> <mi> a </mi> <mn> 4 </mn> </msup> </mrow> <mo> + </mo> <mrow> <mn> 10 </mn> <mo> &#8290; </mo> <msup> <mi> b </mi> <mn> 2 </mn> </msup> <mo> &#8290; </mo> <msup> <mi> a </mi> <mn> 2 </mn> </msup> </mrow> <mo> - </mo> <mrow> <mn> 7 </mn> <mo> &#8290; </mo> <msup> <mi> b </mi> <mn> 4 </mn> </msup> </mrow> </mrow> <mo> ) </mo> </mrow> <mo> &#8290; </mo> <mi> z </mi> <mo> &#8290; </mo> <mrow> <mi> sin </mi> <mo> &#8289; </mo> <mo> ( </mo> <mrow> <mi> b </mi> <mo> &#8290; </mo> <mi> z </mi> </mrow> <mo> ) </mo> </mrow> </mrow> </mrow> <mo> ) </mo> </mrow> </mrow> <mo> ) </mo> </mrow> </mrow> <mo> + </mo> <mrow> <mfrac> <mn> 1 </mn> <mrow> <msup> <mrow> <mo> ( </mo> <mrow> <mi> b </mi> <mo> - </mo> <mi> a </mi> </mrow> <mo> ) </mo> </mrow> <mn> 3 </mn> </msup> <mo> &#8290; </mo> <msup> <mrow> <mo> ( </mo> <mrow> <mi> a </mi> <mo> + </mo> <mi> b </mi> </mrow> <mo> ) </mo> </mrow> <mn> 3 </mn> </msup> </mrow> </mfrac> <mo> &#8290; </mo> <mrow> <mo> ( </mo> <mrow> <mn> 2 </mn> <mo> &#8290; </mo> <msup> <mi> b </mi> <mn> 2 </mn> </msup> <mo> &#8290; </mo> <mrow> <mi> cos </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> <mi> b </mi> <mo> &#8290; </mo> <mrow> <mo> ( </mo> <mrow> <msup> <mi> a </mi> <mn> 4 </mn> </msup> <mo> - </mo> <mrow> <mn> 6 </mn> <mo> &#8290; </mo> <msup> <mi> b </mi> <mn> 2 </mn> </msup> <mo> &#8290; </mo> <msup> <mi> a </mi> <mn> 2 </mn> </msup> </mrow> <mo> + </mo> <mrow> <mn> 5 </mn> <mo> &#8290; </mo> <msup> <mi> b </mi> <mn> 4 </mn> </msup> </mrow> </mrow> <mo> ) </mo> </mrow> <mo> &#8290; </mo> <mi> z </mi> <mo> &#8290; </mo> <mrow> <mi> cos </mi> <mo> &#8289; </mo> <mo> ( </mo> <mrow> <mi> b </mi> <mo> &#8290; </mo> <mi> z </mi> </mrow> <mo> ) </mo> </mrow> </mrow> <mo> + </mo> <mrow> <mrow> <mo> ( </mo> <mrow> <mrow> <mrow> <mo> ( </mo> <mrow> <mrow> <msup> <mi> b </mi> <mn> 2 </mn> </msup> <mo> &#8290; </mo> <msup> <mi> z </mi> <mn> 2 </mn> </msup> </mrow> <mo> - </mo> <mn> 3 </mn> </mrow> <mo> ) </mo> </mrow> <mo> &#8290; </mo> <msup> <mi> a </mi> <mn> 4 </mn> </msup> </mrow> <mo> + </mo> <mrow> <mrow> <mo> ( </mo> <mrow> <mrow> <mn> 6 </mn> <mo> &#8290; </mo> <msup> <mi> b </mi> <mn> 2 </mn> </msup> </mrow> <mo> - </mo> <mrow> <mn> 2 </mn> <mo> &#8290; </mo> <msup> <mi> b </mi> <mn> 4 </mn> </msup> <mo> &#8290; </mo> <msup> <mi> z </mi> <mn> 2 </mn> </msup> </mrow> </mrow> <mo> ) </mo> </mrow> <mo> &#8290; </mo> <msup> <mi> a </mi> <mn> 2 </mn> </msup> </mrow> <mo> + </mo> <mrow> <msup> <mi> b </mi> <mn> 4 </mn> </msup> <mo> &#8290; </mo> <mrow> <mo> ( </mo> <mrow> <mrow> <msup> <mi> b </mi> <mn> 2 </mn> </msup> <mo> &#8290; </mo> <msup> <mi> z </mi> <mn> 2 </mn> </msup> </mrow> <mo> - </mo> <mn> 11 </mn> </mrow> <mo> ) </mo> </mrow> </mrow> </mrow> <mo> ) </mo> </mrow> <mo> &#8290; </mo> <mrow> <mi> sin </mi> <mo> &#8289; </mo> <mo> ( </mo> <mrow> <mi> b </mi> <mo> &#8290; </mo> <mi> z </mi> </mrow> <mo> ) </mo> </mrow> </mrow> </mrow> <mo> ) </mo> </mrow> </mrow> <mo> ) </mo> </mrow> </mrow> <mo> - </mo> <mrow> <mn> 2 </mn> <mo> &#8290; </mo> <mrow> <mi> Ci </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> <mi> b </mi> <mo> &#8290; </mo> <mi> z </mi> <mo> &#8290; </mo> <mrow> <mo> ( </mo> <mrow> <mrow> <msup> <mi> b </mi> <mn> 2 </mn> </msup> <mo> &#8290; </mo> <msup> <mi> z </mi> <mn> 2 </mn> </msup> </mrow> <mo> - </mo> <mn> 6 </mn> </mrow> <mo> ) </mo> </mrow> <mo> &#8290; </mo> <mrow> <mi> cos </mi> <mo> &#8289; </mo> <mo> ( </mo> <mrow> <mi> b </mi> <mo> &#8290; </mo> <mi> z </mi> </mrow> <mo> ) </mo> </mrow> </mrow> <mo> - </mo> <mrow> <mn> 3 </mn> <mo> &#8290; </mo> <mrow> <mo> ( </mo> <mrow> <mrow> <msup> <mi> b </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> sin </mi> <mo> &#8289; </mo> <mo> ( </mo> <mrow> <mi> b </mi> <mo> &#8290; </mo> <mi> z </mi> </mrow> <mo> ) </mo> </mrow> </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> <power /> <ci> z </ci> <cn type='integer'> 3 </cn> </apply> <apply> <sin /> <apply> <times /> <ci> b </ci> <ci> z </ci> </apply> </apply> <apply> <ci> CosIntegral </ci> <apply> <times /> <ci> a </ci> <ci> z </ci> </apply> </apply> </apply> </apply> <apply> <times /> <apply> <times /> <cn type='integer'> 1 </cn> <apply> <power /> <apply> <times /> <cn type='integer'> 2 </cn> <apply> <power /> <ci> b </ci> <cn type='integer'> 4 </cn> </apply> </apply> <cn type='integer'> -1 </cn> </apply> </apply> <apply> <plus /> <apply> <times /> <cn type='integer'> 3 </cn> <imaginaryi /> <apply> <plus /> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <ci> ExpIntegralEi </ci> <apply> <times /> <apply> <times /> <cn type='integer'> -1 </cn> <imaginaryi /> </apply> <apply> <plus /> <ci> a </ci> <apply> <times /> <cn type='integer'> -1 </cn> <ci> b </ci> </apply> </apply> <ci> z </ci> </apply> </apply> </apply> <apply> <ci> ExpIntegralEi </ci> <apply> <times /> <imaginaryi /> <apply> <plus /> <ci> a </ci> <apply> <times /> <cn type='integer'> -1 </cn> <ci> b </ci> </apply> </apply> <ci> z </ci> </apply> </apply> <apply> <ci> ExpIntegralEi </ci> <apply> <times /> <apply> <times /> <cn type='integer'> -1 </cn> <imaginaryi /> </apply> <apply> <plus /> <ci> a </ci> <ci> b </ci> </apply> <ci> z </ci> </apply> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <ci> ExpIntegralEi </ci> <apply> <times /> <imaginaryi /> <apply> <plus /> <ci> a </ci> <ci> b </ci> </apply> <ci> z </ci> </apply> </apply> </apply> </apply> </apply> <apply> <times /> <apply> <times /> <cn type='integer'> 1 </cn> <apply> <power /> <apply> <times /> <apply> <power /> <apply> <plus /> <ci> a </ci> <apply> <times /> <cn type='integer'> -1 </cn> <ci> b </ci> </apply> </apply> <cn type='integer'> 3 </cn> </apply> <apply> <power /> <apply> <plus /> <ci> a </ci> <ci> b </ci> </apply> <cn type='integer'> 3 </cn> </apply> </apply> <cn type='integer'> -1 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> 2 </cn> <ci> a </ci> <ci> b </ci> <apply> <sin /> <apply> <times /> <ci> a </ci> <ci> z </ci> </apply> </apply> <apply> <plus /> <apply> <times /> <apply> <plus /> <apply> <times /> <apply> <plus /> <apply> <times /> <apply> <power /> <ci> b </ci> <cn type='integer'> 2 </cn> </apply> <apply> <power /> <ci> z </ci> <cn type='integer'> 2 </cn> </apply> </apply> <cn type='integer'> -6 </cn> </apply> <apply> <power /> <ci> a </ci> <cn type='integer'> 4 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <cn type='integer'> 2 </cn> <apply> <power /> <ci> b </ci> <cn type='integer'> 2 </cn> </apply> <apply> <plus /> <apply> <times /> <apply> <power /> <ci> b </ci> <cn type='integer'> 2 </cn> </apply> <apply> <power /> <ci> z </ci> <cn type='integer'> 2 </cn> </apply> </apply> <cn type='integer'> -8 </cn> </apply> <apply> <power /> <ci> a </ci> <cn type='integer'> 2 </cn> </apply> </apply> </apply> <apply> <times /> <apply> <power /> <ci> b </ci> <cn type='integer'> 4 </cn> </apply> <apply> <plus /> <apply> <times /> <apply> <power /> <ci> b </ci> <cn type='integer'> 2 </cn> </apply> <apply> <power /> <ci> z </ci> <cn type='integer'> 2 </cn> </apply> </apply> <cn type='integer'> -18 </cn> </apply> </apply> </apply> <apply> <cos /> <apply> <times /> <ci> b </ci> <ci> z </ci> </apply> </apply> </apply> <apply> <times /> <ci> b </ci> <apply> <plus /> <apply> <times /> <cn type='integer'> -3 </cn> <apply> <power /> <ci> a </ci> <cn type='integer'> 4 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> 10 </cn> <apply> <power /> <ci> b </ci> <cn type='integer'> 2 </cn> </apply> <apply> <power /> <ci> a </ci> <cn type='integer'> 2 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <cn type='integer'> 7 </cn> <apply> <power /> <ci> b </ci> <cn type='integer'> 4 </cn> </apply> </apply> </apply> </apply> <ci> z </ci> <apply> <sin /> <apply> <times /> <ci> b </ci> <ci> z </ci> </apply> </apply> </apply> </apply> </apply> </apply> <apply> <times /> <apply> <times /> <cn type='integer'> 1 </cn> <apply> <power /> <apply> <times /> <apply> <power /> <apply> <plus /> <ci> b </ci> <apply> <times /> <cn type='integer'> -1 </cn> <ci> a </ci> </apply> </apply> <cn type='integer'> 3 </cn> </apply> <apply> <power /> <apply> <plus /> <ci> a </ci> <ci> b </ci> </apply> <cn type='integer'> 3 </cn> </apply> </apply> <cn type='integer'> -1 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> 2 </cn> <apply> <power /> <ci> b </ci> <cn type='integer'> 2 </cn> </apply> <apply> <cos /> <apply> <times /> <ci> a </ci> <ci> z </ci> </apply> </apply> <apply> <plus /> <apply> <times /> <ci> b </ci> <apply> <plus /> <apply> <power /> <ci> a </ci> <cn type='integer'> 4 </cn> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <cn type='integer'> 6 </cn> <apply> <power /> <ci> b </ci> <cn type='integer'> 2 </cn> </apply> <apply> <power /> <ci> a </ci> <cn type='integer'> 2 </cn> </apply> </apply> </apply> <apply> <times /> <cn type='integer'> 5 </cn> <apply> <power /> <ci> b </ci> <cn type='integer'> 4 </cn> </apply> </apply> </apply> <ci> z </ci> <apply> <cos /> <apply> <times /> <ci> b </ci> <ci> z </ci> </apply> </apply> </apply> <apply> <times /> <apply> <plus /> <apply> <times /> <apply> <plus /> <apply> <times /> <apply> <power /> <ci> b </ci> <cn type='integer'> 2 </cn> </apply> <apply> <power /> <ci> z </ci> <cn type='integer'> 2 </cn> </apply> </apply> <cn type='integer'> -3 </cn> </apply> <apply> <power /> <ci> a </ci> <cn type='integer'> 4 </cn> </apply> </apply> <apply> <times /> <apply> <plus /> <apply> <times /> <cn type='integer'> 6 </cn> <apply> <power /> <ci> b </ci> <cn type='integer'> 2 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <cn type='integer'> 2 </cn> <apply> <power /> <ci> b </ci> <cn type='integer'> 4 </cn> </apply> <apply> <power /> <ci> z </ci> <cn type='integer'> 2 </cn> </apply> </apply> </apply> </apply> <apply> <power /> <ci> a </ci> <cn type='integer'> 2 </cn> </apply> </apply> <apply> <times /> <apply> <power /> <ci> b </ci> <cn type='integer'> 4 </cn> </apply> <apply> <plus /> <apply> <times /> <apply> <power /> <ci> b </ci> <cn type='integer'> 2 </cn> </apply> <apply> <power /> <ci> z </ci> <cn type='integer'> 2 </cn> </apply> </apply> <cn type='integer'> -11 </cn> </apply> </apply> </apply> <apply> <sin /> <apply> <times /> <ci> b </ci> <ci> z </ci> </apply> </apply> </apply> </apply> </apply> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <cn type='integer'> 2 </cn> <apply> <ci> CosIntegral </ci> <apply> <times /> <ci> a </ci> <ci> z </ci> </apply> </apply> <apply> <plus /> <apply> <times /> <ci> b </ci> <ci> z </ci> <apply> <plus /> <apply> <times /> <apply> <power /> <ci> b </ci> <cn type='integer'> 2 </cn> </apply> <apply> <power /> <ci> z </ci> <cn type='integer'> 2 </cn> </apply> </apply> <cn type='integer'> -6 </cn> </apply> <apply> <cos /> <apply> <times /> <ci> b </ci> <ci> z </ci> </apply> </apply> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <cn type='integer'> 3 </cn> <apply> <plus /> <apply> <times /> <apply> <power /> <ci> b </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> <sin /> <apply> <times /> <ci> b </ci> <ci> z </ci> </apply> </apply> </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[RowBox[List[SuperscriptBox["z_", "3"], " ", RowBox[List["Sin", "[", RowBox[List["b_", " ", "z_"]], "]"]], " ", RowBox[List["CosIntegral", "[", RowBox[List["a_", " ", "z_"]], "]"]]]], RowBox[List["\[DifferentialD]", "z_"]]]]]], "]"]], "\[RuleDelayed]", FractionBox[RowBox[List[RowBox[List["3", " ", "\[ImaginaryI]", " ", RowBox[List["(", RowBox[List[RowBox[List["-", RowBox[List["ExpIntegralEi", "[", RowBox[List[RowBox[List["-", "\[ImaginaryI]"]], " ", RowBox[List["(", RowBox[List["a", "-", "b"]], ")"]], " ", "z"]], "]"]]]], "+", RowBox[List["ExpIntegralEi", "[", RowBox[List["\[ImaginaryI]", " ", RowBox[List["(", RowBox[List["a", "-", "b"]], ")"]], " ", "z"]], "]"]], "+", RowBox[List["ExpIntegralEi", "[", RowBox[List[RowBox[List["-", "\[ImaginaryI]"]], " ", RowBox[List["(", RowBox[List["a", "+", "b"]], ")"]], " ", "z"]], "]"]], "-", RowBox[List["ExpIntegralEi", "[", RowBox[List["\[ImaginaryI]", " ", RowBox[List["(", RowBox[List["a", "+", "b"]], ")"]], " ", "z"]], "]"]]]], ")"]]]], "+", FractionBox[RowBox[List["2", " ", "a", " ", "b", " ", RowBox[List["Sin", "[", RowBox[List["a", " ", "z"]], "]"]], " ", RowBox[List["(", RowBox[List[RowBox[List[RowBox[List["(", RowBox[List[RowBox[List[SuperscriptBox["b", "4"], " ", RowBox[List["(", RowBox[List[RowBox[List["-", "18"]], "+", RowBox[List[SuperscriptBox["b", "2"], " ", SuperscriptBox["z", "2"]]]]], ")"]]]], "-", RowBox[List["2", " ", SuperscriptBox["a", "2"], " ", SuperscriptBox["b", "2"], " ", RowBox[List["(", RowBox[List[RowBox[List["-", "8"]], "+", RowBox[List[SuperscriptBox["b", "2"], " ", SuperscriptBox["z", "2"]]]]], ")"]]]], "+", RowBox[List[SuperscriptBox["a", "4"], " ", RowBox[List["(", RowBox[List[RowBox[List["-", "6"]], "+", RowBox[List[SuperscriptBox["b", "2"], " ", SuperscriptBox["z", "2"]]]]], ")"]]]]]], ")"]], " ", RowBox[List["Cos", "[", RowBox[List["b", " ", "z"]], "]"]]]], "+", RowBox[List["b", " ", RowBox[List["(", RowBox[List[RowBox[List[RowBox[List["-", "3"]], " ", SuperscriptBox["a", "4"]]], "+", RowBox[List["10", " ", SuperscriptBox["a", "2"], " ", SuperscriptBox["b", "2"]]], "-", RowBox[List["7", " ", SuperscriptBox["b", "4"]]]]], ")"]], " ", "z", " ", RowBox[List["Sin", "[", RowBox[List["b", " ", "z"]], "]"]]]]]], ")"]]]], RowBox[List[SuperscriptBox[RowBox[List["(", RowBox[List["a", "-", "b"]], ")"]], "3"], " ", SuperscriptBox[RowBox[List["(", RowBox[List["a", "+", "b"]], ")"]], "3"]]]], "-", RowBox[List["2", " ", RowBox[List["CosIntegral", "[", RowBox[List["a", " ", "z"]], "]"]], " ", RowBox[List["(", RowBox[List[RowBox[List["b", " ", "z", " ", RowBox[List["(", RowBox[List[RowBox[List["-", "6"]], "+", RowBox[List[SuperscriptBox["b", "2"], " ", SuperscriptBox["z", "2"]]]]], ")"]], " ", RowBox[List["Cos", "[", RowBox[List["b", " ", "z"]], "]"]]]], "-", RowBox[List["3", " ", RowBox[List["(", RowBox[List[RowBox[List["-", "2"]], "+", RowBox[List[SuperscriptBox["b", "2"], " ", SuperscriptBox["z", "2"]]]]], ")"]], " ", RowBox[List["Sin", "[", RowBox[List["b", " ", "z"]], "]"]]]]]], ")"]]]], "+", FractionBox[RowBox[List["2", " ", SuperscriptBox["b", "2"], " ", RowBox[List["Cos", "[", RowBox[List["a", " ", "z"]], "]"]], " ", RowBox[List["(", RowBox[List[RowBox[List["b", " ", RowBox[List["(", RowBox[List[SuperscriptBox["a", "4"], "-", RowBox[List["6", " ", SuperscriptBox["a", "2"], " ", SuperscriptBox["b", "2"]]], "+", RowBox[List["5", " ", SuperscriptBox["b", "4"]]]]], ")"]], " ", "z", " ", RowBox[List["Cos", "[", RowBox[List["b", " ", "z"]], "]"]]]], "+", RowBox[List[RowBox[List["(", RowBox[List[RowBox[List[SuperscriptBox["b", "4"], " ", RowBox[List["(", RowBox[List[RowBox[List["-", "11"]], "+", RowBox[List[SuperscriptBox["b", "2"], " ", SuperscriptBox["z", "2"]]]]], ")"]]]], "+", RowBox[List[SuperscriptBox["a", "4"], " ", RowBox[List["(", RowBox[List[RowBox[List["-", "3"]], "+", RowBox[List[SuperscriptBox["b", "2"], " ", SuperscriptBox["z", "2"]]]]], ")"]]]], "+", RowBox[List[SuperscriptBox["a", "2"], " ", RowBox[List["(", RowBox[List[RowBox[List["6", " ", SuperscriptBox["b", "2"]]], "-", RowBox[List["2", " ", SuperscriptBox["b", "4"], " ", SuperscriptBox["z", "2"]]]]], ")"]]]]]], ")"]], " ", RowBox[List["Sin", "[", RowBox[List["b", " ", "z"]], "]"]]]]]], ")"]]]], RowBox[List[SuperscriptBox[RowBox[List["(", RowBox[List[RowBox[List["-", "a"]], "+", "b"]], ")"]], "3"], " ", SuperscriptBox[RowBox[List["(", RowBox[List["a", "+", "b"]], ")"]], "3"]]]]]], RowBox[List["2", " ", SuperscriptBox["b", "4"]]]]]]]]


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





2001-10-29