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 CosIntegral

 http://functions.wolfram.com/06.38.21.0027.01

 Input Form

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

 Standard Form

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

 MathML Form

 z 2 sin ( b z ) Ci ( a z ) z - 1 2 b 3 ( Ei ( - ( a - b ) z ) + Ei ( ( a - b ) z ) + Ei ( - ( a + b ) z ) + Ei ( ( a + b ) z ) ) + cos ( a z ) ( b ( b 2 - a 2 ) z sin ( b z ) - ( a 2 - 3 b 2 ) cos ( b z ) ) ( a - b ) 2 b ( a + b ) 2 + a sin ( a z ) ( b ( a 2 - b 2 ) z cos ( b z ) - 2 ( a 2 - 2 b 2 ) sin ( b z ) ) ( a - b ) 2 b 2 ( a + b ) 2 - Ci ( a z ) ( ( b 2 z 2 - 2 ) cos ( b z ) - 2 b z sin ( b z ) ) b 3 z z 2 b z CosIntegral a z -1 1 2 b 3 -1 ExpIntegralEi -1 a -1 b z ExpIntegralEi a -1 b z ExpIntegralEi -1 a b z ExpIntegralEi a b z a z b b 2 -1 a 2 z b z -1 a 2 -1 3 b 2 b z a -1 b 2 b a b 2 -1 a a z b a 2 -1 b 2 z b z -1 2 a 2 -1 2 b 2 b z a -1 b 2 b 2 a b 2 -1 -1 CosIntegral a z b 2 z 2 -2 b z -1 2 b z b z b 3 -1 [/itex]

 Rule Form

 Cell[BoxData[RowBox[List[RowBox[List["HoldPattern", "[", RowBox[List["\[Integral]", RowBox[List[RowBox[List[SuperscriptBox["z_", "2"], " ", RowBox[List["Sin", "[", RowBox[List["b_", " ", "z_"]], "]"]], " ", RowBox[List["CosIntegral", "[", RowBox[List["a_", " ", "z_"]], "]"]]]], RowBox[List["\[DifferentialD]", "z_"]]]]]], "]"]], "\[RuleDelayed]", RowBox[List[RowBox[List["-", FractionBox[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["2", " ", SuperscriptBox["b", "3"]]]]]], "+", FractionBox[RowBox[List["a", " ", RowBox[List["Sin", "[", RowBox[List["a", " ", "z"]], "]"]], " ", RowBox[List["(", RowBox[List[RowBox[List["b", " ", RowBox[List["(", RowBox[List[SuperscriptBox["a", "2"], "-", SuperscriptBox["b", "2"]]], ")"]], " ", "z", " ", RowBox[List["Cos", "[", RowBox[List["b", " ", "z"]], "]"]]]], "-", RowBox[List["2", " ", RowBox[List["(", RowBox[List[SuperscriptBox["a", "2"], "-", RowBox[List["2", " ", SuperscriptBox["b", "2"]]]]], ")"]], " ", RowBox[List["Sin", "[", RowBox[List["b", " ", "z"]], "]"]]]]]], ")"]]]], RowBox[List[SuperscriptBox[RowBox[List["(", RowBox[List["a", "-", "b"]], ")"]], "2"], " ", SuperscriptBox["b", "2"], " ", SuperscriptBox[RowBox[List["(", RowBox[List["a", "+", "b"]], ")"]], "2"]]]], "-", FractionBox[RowBox[List[RowBox[List["CosIntegral", "[", RowBox[List["a", " ", "z"]], "]"]], " ", RowBox[List["(", RowBox[List[RowBox[List[RowBox[List["(", RowBox[List[RowBox[List["-", "2"]], "+", RowBox[List[SuperscriptBox["b", "2"], " ", SuperscriptBox["z", "2"]]]]], ")"]], " ", RowBox[List["Cos", "[", RowBox[List["b", " ", "z"]], "]"]]]], "-", RowBox[List["2", " ", "b", " ", "z", " ", RowBox[List["Sin", "[", RowBox[List["b", " ", "z"]], "]"]]]]]], ")"]]]], SuperscriptBox["b", "3"]], "+", FractionBox[RowBox[List[RowBox[List["Cos", "[", RowBox[List["a", " ", "z"]], "]"]], " ", RowBox[List["(", RowBox[List[RowBox[List[RowBox[List["-", RowBox[List["(", RowBox[List[SuperscriptBox["a", "2"], "-", RowBox[List["3", " ", SuperscriptBox["b", "2"]]]]], ")"]]]], " ", RowBox[List["Cos", "[", RowBox[List["b", " ", "z"]], "]"]]]], "+", RowBox[List["b", " ", RowBox[List["(", RowBox[List[RowBox[List["-", SuperscriptBox["a", "2"]]], "+", SuperscriptBox["b", "2"]]], ")"]], " ", "z", " ", RowBox[List["Sin", "[", RowBox[List["b", " ", "z"]], "]"]]]]]], ")"]]]], RowBox[List[SuperscriptBox[RowBox[List["(", RowBox[List["a", "-", "b"]], ")"]], "2"], " ", "b", " ", SuperscriptBox[RowBox[List["(", RowBox[List["a", "+", "b"]], ")"]], "2"]]]]]]]]]]

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

 2001-10-29