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SinIntegral






Mathematica Notation

Traditional Notation









Gamma, Beta, Erf > SinIntegral[z] > Integration > Indefinite integration > Involving one direct function and elementary functions > Involving exponential function and a power function > Involving exp and power





http://functions.wolfram.com/06.37.21.0017.01









  


  










Input Form





Integrate[z E^(b z) SinIntegral[a z], z] == (1/(2 b^2 (a^2 + b^2))) (2 a b E^(b z) Cos[a z] + I (a^2 + b^2) ExpIntegralEi[((-I) a + b) z] - I a^2 ExpIntegralEi[(I a + b) z] - I b^2 ExpIntegralEi[(I a + b) z] - 2 b^2 E^(b z) Sin[a z] + 2 (a^2 + b^2) E^(b z) (-1 + b z) SinIntegral[a z])










Standard Form





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MathML Form







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Rule Form





Cell[BoxData[RowBox[List[RowBox[List["HoldPattern", "[", RowBox[List["\[Integral]", RowBox[List[RowBox[List["z_", " ", SuperscriptBox["\[ExponentialE]", RowBox[List["b_", " ", "z_"]]], " ", RowBox[List["SinIntegral", "[", RowBox[List["a_", " ", "z_"]], "]"]]]], RowBox[List["\[DifferentialD]", "z_"]]]]]], "]"]], "\[RuleDelayed]", FractionBox[RowBox[List[RowBox[List["2", " ", "a", " ", "b", " ", SuperscriptBox["\[ExponentialE]", RowBox[List["b", " ", "z"]]], " ", RowBox[List["Cos", "[", RowBox[List["a", " ", "z"]], "]"]]]], "+", RowBox[List["\[ImaginaryI]", " ", RowBox[List["(", RowBox[List[SuperscriptBox["a", "2"], "+", SuperscriptBox["b", "2"]]], ")"]], " ", RowBox[List["ExpIntegralEi", "[", RowBox[List[RowBox[List["(", RowBox[List[RowBox[List[RowBox[List["-", "\[ImaginaryI]"]], " ", "a"]], "+", "b"]], ")"]], " ", "z"]], "]"]]]], "-", RowBox[List["\[ImaginaryI]", " ", SuperscriptBox["a", "2"], " ", RowBox[List["ExpIntegralEi", "[", RowBox[List[RowBox[List["(", RowBox[List[RowBox[List["\[ImaginaryI]", " ", "a"]], "+", "b"]], ")"]], " ", "z"]], "]"]]]], "-", RowBox[List["\[ImaginaryI]", " ", SuperscriptBox["b", "2"], " ", RowBox[List["ExpIntegralEi", "[", RowBox[List[RowBox[List["(", RowBox[List[RowBox[List["\[ImaginaryI]", " ", "a"]], "+", "b"]], ")"]], " ", "z"]], "]"]]]], "-", RowBox[List["2", " ", SuperscriptBox["b", "2"], " ", SuperscriptBox["\[ExponentialE]", RowBox[List["b", " ", "z"]]], " ", RowBox[List["Sin", "[", RowBox[List["a", " ", "z"]], "]"]]]], "+", RowBox[List["2", " ", RowBox[List["(", RowBox[List[SuperscriptBox["a", "2"], "+", SuperscriptBox["b", "2"]]], ")"]], " ", SuperscriptBox["\[ExponentialE]", RowBox[List["b", " ", "z"]]], " ", RowBox[List["(", RowBox[List[RowBox[List["-", "1"]], "+", RowBox[List["b", " ", "z"]]]], ")"]], " ", RowBox[List["SinIntegral", "[", RowBox[List["a", " ", "z"]], "]"]]]]]], RowBox[List["2", " ", SuperscriptBox["b", "2"], " ", RowBox[List["(", RowBox[List[SuperscriptBox["a", "2"], "+", SuperscriptBox["b", "2"]]], ")"]]]]]]]]]










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





2001-10-29