|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
http://functions.wolfram.com/01.06.21.0153.01
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Integrate[Sin[z]/(z^2 - 1), z] ==
(1/2) (CosIntegral[1 - z] Sin[1] + CosIntegral[1 + z] Sin[1] -
Cos[1] (SinIntegral[1 - z] + SinIntegral[1 + z]))
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Cell[BoxData[RowBox[List[RowBox[List["\[Integral]", RowBox[List[FractionBox[RowBox[List["Sin", "[", "z", "]"]], RowBox[List[SuperscriptBox["z", "2"], "-", "1"]]], RowBox[List["\[DifferentialD]", "z"]]]]]], "\[Equal]", RowBox[List[FractionBox["1", "2"], " ", RowBox[List["(", RowBox[List[RowBox[List[RowBox[List["CosIntegral", "[", RowBox[List["1", "-", "z"]], "]"]], " ", RowBox[List["Sin", "[", "1", "]"]]]], "+", RowBox[List[RowBox[List["CosIntegral", "[", RowBox[List["1", "+", "z"]], "]"]], " ", RowBox[List["Sin", "[", "1", "]"]]]], "-", RowBox[List[RowBox[List["Cos", "[", "1", "]"]], " ", RowBox[List["(", RowBox[List[RowBox[List["SinIntegral", "[", RowBox[List["1", "-", "z"]], "]"]], "+", RowBox[List["SinIntegral", "[", RowBox[List["1", "+", "z"]], "]"]]]], ")"]]]]]], ")"]]]]]]]]
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
<math xmlns='http://www.w3.org/1998/Math/MathML' mathematica:form='TraditionalForm' xmlns:mathematica='http://www.wolfram.com/XML/'> <semantics> <mrow> <mrow> <mo> ∫ </mo> <mrow> <mfrac> <mrow> <mi> sin </mi> <mo> ⁡ </mo> <mo> ( </mo> <mi> z </mi> <mo> ) </mo> </mrow> <mrow> <msup> <mi> z </mi> <mn> 2 </mn> </msup> <mo> - </mo> <mn> 1 </mn> </mrow> </mfrac> <mo> ⁢ </mo> <mrow> <mo> ⅆ </mo> <mi> z </mi> </mrow> </mrow> </mrow> <mo> ⩵ </mo> <mrow> <mfrac> <mn> 1 </mn> <mn> 2 </mn> </mfrac> <mo> ⁢ </mo> <mrow> <mo> ( </mo> <mrow> <mrow> <mrow> <mi> sin </mi> <mo> ⁡ </mo> <mo> ( </mo> <mn> 1 </mn> <mo> ) </mo> </mrow> <mo> ⁢ </mo> <mrow> <mi> Ci </mi> <mo> ⁡ </mo> <mo> ( </mo> <mrow> <mn> 1 </mn> <mo> - </mo> <mi> z </mi> </mrow> <mo> ) </mo> </mrow> </mrow> <mo> - </mo> <mrow> <mrow> <mi> cos </mi> <mo> ⁡ </mo> <mo> ( </mo> <mn> 1 </mn> <mo> ) </mo> </mrow> <mo> ⁢ </mo> <mrow> <mo> ( </mo> <mrow> <mrow> <mi> Si </mi> <mo> ⁡ </mo> <mo> ( </mo> <mrow> <mn> 1 </mn> <mo> - </mo> <mi> z </mi> </mrow> <mo> ) </mo> </mrow> <mo> + </mo> <mrow> <mi> Si </mi> <mo> ⁡ </mo> <mo> ( </mo> <mrow> <mi> z </mi> <mo> + </mo> <mn> 1 </mn> </mrow> <mo> ) </mo> </mrow> </mrow> <mo> ) </mo> </mrow> </mrow> <mo> + </mo> <mrow> <mrow> <mi> Ci </mi> <mo> ⁡ </mo> <mo> ( </mo> <mrow> <mi> z </mi> <mo> + </mo> <mn> 1 </mn> </mrow> <mo> ) </mo> </mrow> <mo> ⁢ </mo> <mrow> <mi> sin </mi> <mo> ⁡ </mo> <mo> ( </mo> <mn> 1 </mn> <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> <sin /> <ci> z </ci> </apply> <apply> <power /> <apply> <plus /> <apply> <power /> <ci> z </ci> <cn type='integer'> 2 </cn> </apply> <cn type='integer'> -1 </cn> </apply> <cn type='integer'> -1 </cn> </apply> </apply> </apply> <apply> <times /> <cn type='rational'> 1 <sep /> 2 </cn> <apply> <plus /> <apply> <times /> <apply> <sin /> <cn type='integer'> 1 </cn> </apply> <apply> <ci> CosIntegral </ci> <apply> <plus /> <cn type='integer'> 1 </cn> <apply> <times /> <cn type='integer'> -1 </cn> <ci> z </ci> </apply> </apply> </apply> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <apply> <cos /> <cn type='integer'> 1 </cn> </apply> <apply> <plus /> <apply> <ci> SinIntegral </ci> <apply> <plus /> <cn type='integer'> 1 </cn> <apply> <times /> <cn type='integer'> -1 </cn> <ci> z </ci> </apply> </apply> </apply> <apply> <ci> SinIntegral </ci> <apply> <plus /> <ci> z </ci> <cn type='integer'> 1 </cn> </apply> </apply> </apply> </apply> </apply> <apply> <times /> <apply> <ci> CosIntegral </ci> <apply> <plus /> <ci> z </ci> <cn type='integer'> 1 </cn> </apply> </apply> <apply> <sin /> <cn type='integer'> 1 </cn> </apply> </apply> </apply> </apply> </apply> </annotation-xml> </semantics> </math>
|
|
|
|
|
|
|
|
|
|
| |
|
|
|
|
| Cell[BoxData[RowBox[List[RowBox[List["HoldPattern", "[", RowBox[List["\[Integral]", RowBox[List[FractionBox[RowBox[List["Sin", "[", "z_", "]"]], RowBox[List[SuperscriptBox["z_", "2"], "-", "1"]]], RowBox[List["\[DifferentialD]", "z_"]]]]]], "]"]], "\[RuleDelayed]", RowBox[List[FractionBox["1", "2"], " ", RowBox[List["(", RowBox[List[RowBox[List[RowBox[List["CosIntegral", "[", RowBox[List["1", "-", "z"]], "]"]], " ", RowBox[List["Sin", "[", "1", "]"]]]], "+", RowBox[List[RowBox[List["CosIntegral", "[", RowBox[List["1", "+", "z"]], "]"]], " ", RowBox[List["Sin", "[", "1", "]"]]]], "-", RowBox[List[RowBox[List["Cos", "[", "1", "]"]], " ", RowBox[List["(", RowBox[List[RowBox[List["SinIntegral", "[", RowBox[List["1", "-", "z"]], "]"]], "+", RowBox[List["SinIntegral", "[", RowBox[List["1", "+", "z"]], "]"]]]], ")"]]]]]], ")"]]]]]]]] |
|
|
|
|
|
|
|
|
|
|
Date Added to functions.wolfram.com (modification date)
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|