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http://functions.wolfram.com/01.06.21.1040.01
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Integrate[Sin[a z + b]^2/z, z] == (1/2) ((-Cos[2 b]) CosIntegral[2 a z] +
Log[z] + Sin[2 b] SinIntegral[2 a z])
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Cell[BoxData[RowBox[List[RowBox[List["\[Integral]", RowBox[List[FractionBox[SuperscriptBox[RowBox[List["Sin", "[", RowBox[List[RowBox[List["a", " ", "z"]], "+", "b"]], "]"]], "2"], "z"], RowBox[List["\[DifferentialD]", "z"]]]]]], "\[Equal]", RowBox[List[FractionBox["1", "2"], " ", RowBox[List["(", RowBox[List[RowBox[List[RowBox[List["-", RowBox[List["Cos", "[", RowBox[List["2", " ", "b"]], "]"]]]], " ", RowBox[List["CosIntegral", "[", RowBox[List["2", " ", "a", " ", "z"]], "]"]]]], "+", RowBox[List["Log", "[", "z", "]"]], "+", RowBox[List[RowBox[List["Sin", "[", RowBox[List["2", " ", "b"]], "]"]], " ", RowBox[List["SinIntegral", "[", RowBox[List["2", " ", "a", " ", "z"]], "]"]]]]]], ")"]]]]]]]]
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<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> <msup> <mi> sin </mi> <mn> 2 </mn> </msup> <mo> ( </mo> <mrow> <mrow> <mi> a </mi> <mo> ⁢ </mo> <mi> z </mi> </mrow> <mo> + </mo> <mi> b </mi> </mrow> <mo> ) </mo> </mrow> <mi> z </mi> </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> <mo> - </mo> <mrow> <mi> cos </mi> <mo> ⁡ </mo> <mo> ( </mo> <mrow> <mn> 2 </mn> <mo> ⁢ </mo> <mi> b </mi> </mrow> <mo> ) </mo> </mrow> </mrow> <mo> ⁢ </mo> <mrow> <mi> Ci </mi> <mo> ⁡ </mo> <mo> ( </mo> <mrow> <mn> 2 </mn> <mo> ⁢ </mo> <mi> a </mi> <mo> ⁢ </mo> <mi> z </mi> </mrow> <mo> ) </mo> </mrow> </mrow> <mo> + </mo> <mrow> <mi> log </mi> <mo> ⁡ </mo> <mo> ( </mo> <mi> z </mi> <mo> ) </mo> </mrow> <mo> + </mo> <mrow> <mrow> <mi> sin </mi> <mo> ⁡ </mo> <mo> ( </mo> <mrow> <mn> 2 </mn> <mo> ⁢ </mo> <mi> b </mi> </mrow> <mo> ) </mo> </mrow> <mo> ⁢ </mo> <mrow> <mi> Si </mi> <mo> ⁡ </mo> <mo> ( </mo> <mrow> <mn> 2 </mn> <mo> ⁢ </mo> <mi> a </mi> <mo> ⁢ </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 /> <apply> <sin /> <apply> <plus /> <apply> <times /> <ci> a </ci> <ci> z </ci> </apply> <ci> b </ci> </apply> </apply> <cn type='integer'> 2 </cn> </apply> <apply> <power /> <ci> z </ci> <cn type='integer'> -1 </cn> </apply> </apply> </apply> <apply> <times /> <cn type='rational'> 1 <sep /> 2 </cn> <apply> <plus /> <apply> <times /> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <cos /> <apply> <times /> <cn type='integer'> 2 </cn> <ci> b </ci> </apply> </apply> </apply> <apply> <ci> CosIntegral </ci> <apply> <times /> <cn type='integer'> 2 </cn> <ci> a </ci> <ci> z </ci> </apply> </apply> </apply> <apply> <ln /> <ci> z </ci> </apply> <apply> <times /> <apply> <sin /> <apply> <times /> <cn type='integer'> 2 </cn> <ci> b </ci> </apply> </apply> <apply> <ci> SinIntegral </ci> <apply> <times /> <cn type='integer'> 2 </cn> <ci> a </ci> <ci> z </ci> </apply> </apply> </apply> </apply> </apply> </apply> </annotation-xml> </semantics> </math>
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| Cell[BoxData[RowBox[List[RowBox[List["HoldPattern", "[", RowBox[List["\[Integral]", RowBox[List[FractionBox[SuperscriptBox[RowBox[List["Sin", "[", RowBox[List[RowBox[List["a_", " ", "z_"]], "+", "b_"]], "]"]], "2"], "z_"], RowBox[List["\[DifferentialD]", "z_"]]]]]], "]"]], "\[RuleDelayed]", RowBox[List[FractionBox["1", "2"], " ", RowBox[List["(", RowBox[List[RowBox[List[RowBox[List["-", RowBox[List["Cos", "[", RowBox[List["2", " ", "b"]], "]"]]]], " ", RowBox[List["CosIntegral", "[", RowBox[List["2", " ", "a", " ", "z"]], "]"]]]], "+", RowBox[List["Log", "[", "z", "]"]], "+", RowBox[List[RowBox[List["Sin", "[", RowBox[List["2", " ", "b"]], "]"]], " ", RowBox[List["SinIntegral", "[", RowBox[List["2", " ", "a", " ", "z"]], "]"]]]]]], ")"]]]]]]]] |
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Date Added to functions.wolfram.com (modification date)
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