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 SinIntegral

 http://functions.wolfram.com/06.37.21.0027.01

 Input Form

 Integrate[z^2 Sin[b z] SinIntegral[a z], z] == (-(1/(2 b^3))) (I (ExpIntegralEi[(-I) (a - b) z] + ((-(a^2 - b^2)^2) (ExpIntegralEi[I (a - b) z] - ExpIntegralEi[ (-I) (a + b) z] + ExpIntegralEi[I (a + b) z]) + 2 I b^2 Cos[b z] (a (-a^2 + b^2) z Cos[a z] - (a^2 - 3 b^2) Sin[a z]) + 2 I b (2 a (a^2 - 2 b^2) Cos[a z] + b^2 (-a^2 + b^2) z Sin[a z]) Sin[b z])/((a - b)^2 (a + b)^2) + I (Gamma[3, (-I) b z] + Gamma[3, I b z]) SinIntegral[a z]))

 Standard Form

 Cell[BoxData[RowBox[List[RowBox[List["\[Integral]", RowBox[List[SuperscriptBox["z", "2"], " ", RowBox[List["Sin", "[", RowBox[List["b", " ", "z"]], "]"]], RowBox[List["SinIntegral", "[", RowBox[List["a", " ", "z"]], "]"]], RowBox[List["\[DifferentialD]", "z"]]]]]], "\[Equal]", RowBox[List[RowBox[List["-", FractionBox["1", RowBox[List["2", " ", SuperscriptBox["b", "3"]]]]]], RowBox[List["(", RowBox[List["\[ImaginaryI]", " ", RowBox[List["(", RowBox[List[RowBox[List["ExpIntegralEi", "[", RowBox[List[RowBox[List["-", "\[ImaginaryI]"]], " ", RowBox[List["(", RowBox[List["a", "-", "b"]], ")"]], " ", "z"]], "]"]], "+", RowBox[List[RowBox[List["(", RowBox[List[RowBox[List[RowBox[List["-", SuperscriptBox[RowBox[List["(", RowBox[List[SuperscriptBox["a", "2"], "-", SuperscriptBox["b", "2"]]], ")"]], "2"]]], " ", RowBox[List["(", RowBox[List[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["2", " ", "\[ImaginaryI]", " ", SuperscriptBox["b", "2"], " ", RowBox[List["Cos", "[", RowBox[List["b", " ", "z"]], "]"]], " ", RowBox[List["(", RowBox[List[RowBox[List["a", " ", RowBox[List["(", RowBox[List[RowBox[List["-", SuperscriptBox["a", "2"]]], "+", SuperscriptBox["b", "2"]]], ")"]], " ", "z", " ", RowBox[List["Cos", "[", RowBox[List["a", " ", "z"]], "]"]]]], "-", RowBox[List[RowBox[List["(", RowBox[List[SuperscriptBox["a", "2"], "-", RowBox[List["3", " ", SuperscriptBox["b", "2"]]]]], ")"]], " ", RowBox[List["Sin", "[", RowBox[List["a", " ", "z"]], "]"]]]]]], ")"]]]], "+", RowBox[List["2", " ", "\[ImaginaryI]", " ", "b", " ", RowBox[List["(", RowBox[List[RowBox[List["2", " ", "a", " ", RowBox[List["(", RowBox[List[SuperscriptBox["a", "2"], "-", RowBox[List["2", " ", SuperscriptBox["b", "2"]]]]], ")"]], " ", RowBox[List["Cos", "[", RowBox[List["a", " ", "z"]], "]"]]]], "+", RowBox[List[SuperscriptBox["b", "2"], " ", RowBox[List["(", RowBox[List[RowBox[List["-", SuperscriptBox["a", "2"]]], "+", SuperscriptBox["b", "2"]]], ")"]], " ", "z", " ", RowBox[List["Sin", "[", RowBox[List["a", " ", "z"]], "]"]]]]]], ")"]], " ", RowBox[List["Sin", "[", RowBox[List["b", " ", "z"]], "]"]]]]]], ")"]], "/", RowBox[List["(", RowBox[List[SuperscriptBox[RowBox[List["(", RowBox[List["a", "-", "b"]], ")"]], "2"], " ", SuperscriptBox[RowBox[List["(", RowBox[List["a", "+", "b"]], ")"]], "2"]]], ")"]]]], "+", RowBox[List["\[ImaginaryI]", " ", RowBox[List["(", RowBox[List[RowBox[List["Gamma", "[", RowBox[List["3", ",", RowBox[List[RowBox[List["-", "\[ImaginaryI]"]], " ", "b", " ", "z"]]]], "]"]], "+", RowBox[List["Gamma", "[", RowBox[List["3", ",", RowBox[List["\[ImaginaryI]", " ", "b", " ", "z"]]]], "]"]]]], ")"]], " ", RowBox[List["SinIntegral", "[", RowBox[List["a", " ", "z"]], "]"]]]]]], ")"]]]], ")"]]]]]]]]

 MathML Form

 z 2 sin ( b z ) Si ( a z ) z - 1 2 b 3 ( ( Ei ( - ( a - b ) z ) + 1 ( a - b ) 2 ( a + b ) 2 ( 2 cos ( b z ) ( a ( b 2 - a 2 ) z cos ( a z ) - ( a 2 - 3 b 2 ) sin ( a z ) ) b 2 + 2 ( ( b 2 - a 2 ) z sin ( a z ) b 2 + 2 a ( a 2 - 2 b 2 ) cos ( a z ) ) sin ( b z ) b - ( a 2 - b 2 ) 2 ( Ei ( ( a - b ) z ) - Ei ( - ( a + b ) z ) + Ei ( ( a + b ) z ) ) ) + ( Γ ( 3 , - b z ) + Γ ( 3 , b z ) ) Si ( a z ) ) ) z z 2 b z SinIntegral a z -1 1 2 b 3 -1 ExpIntegralEi -1 a -1 b z 1 a -1 b 2 a b 2 -1 2 b z a b 2 -1 a 2 z a z -1 a 2 -1 3 b 2 a z b 2 2 b 2 -1 a 2 z a z b 2 2 a a 2 -1 2 b 2 a z b z b -1 a 2 -1 b 2 2 ExpIntegralEi a -1 b z -1 ExpIntegralEi -1 a b z ExpIntegralEi a b z Gamma 3 -1 b z Gamma 3 b z SinIntegral a z [/itex]

 Rule Form

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

 2001-10-29