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 CosIntegral

 http://functions.wolfram.com/06.38.21.0064.01

 Input Form

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

 Standard Form

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 MathML Form

 z 2 Ei ( b z ) Ci ( a z ) z 1 3 ( - ( a 2 - 2 b 2 ) b z cos ( a z ) a 2 b ( a 2 + b 2 ) + ( a 3 - b 3 ) Ei ( ( b - a ) z ) + ( a 3 + b 3 ) Ei ( ( b + a ) z ) a 3 b 3 + b z ( ( b z - 2 ) a 2 + b 2 ( b z + 1 ) ) sin ( a z ) a b 2 ( a 2 + b 2 ) + 1 a 3 ( Ei ( b z ) ( a 3 Ci ( a z ) z 3 - 2 a cos ( a z ) z + ( 2 - a 2 z 2 ) sin ( a z ) ) ) - b z ( b 2 z 2 - 2 b z + 2 ) Ci ( a z ) b 3 ) z z 2 ExpIntegralEi b z CosIntegral a z 1 3 -1 a 2 -1 2 b 2 b z a z a 2 b a 2 b 2 -1 a 3 -1 b 3 ExpIntegralEi b -1 a z a 3 b 3 ExpIntegralEi b a z a 3 b 3 -1 b z b z -2 a 2 b 2 b z 1 a z a b 2 a 2 b 2 -1 1 a 3 -1 ExpIntegralEi b z a 3 CosIntegral a z z 3 -1 2 a a z z 2 -1 a 2 z 2 a z -1 b z b 2 z 2 -1 2 b z 2 CosIntegral a 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["ExpIntegralEi", "[", RowBox[List["b_", " ", "z_"]], "]"]], " ", RowBox[List["CosIntegral", "[", RowBox[List["a_", " ", "z_"]], "]"]]]], RowBox[List["\[DifferentialD]", "z_"]]]]]], "]"]], "\[RuleDelayed]", RowBox[List[FractionBox["1", "3"], " ", RowBox[List["(", RowBox[List[RowBox[List["-", FractionBox[RowBox[List[RowBox[List["(", RowBox[List[SuperscriptBox["a", "2"], "-", RowBox[List["2", " ", SuperscriptBox["b", "2"]]]]], ")"]], " ", SuperscriptBox["\[ExponentialE]", RowBox[List["b", " ", "z"]]], " ", RowBox[List["Cos", "[", RowBox[List["a", " ", "z"]], "]"]]]], RowBox[List[SuperscriptBox["a", "2"], " ", "b", " ", RowBox[List["(", RowBox[List[SuperscriptBox["a", "2"], "+", SuperscriptBox["b", "2"]]], ")"]]]]]]], "-", FractionBox[RowBox[List[SuperscriptBox["\[ExponentialE]", RowBox[List["b", " ", "z"]]], " ", RowBox[List["(", RowBox[List["2", "-", RowBox[List["2", " ", "b", " ", "z"]], "+", RowBox[List[SuperscriptBox["b", "2"], " ", SuperscriptBox["z", "2"]]]]], ")"]], " ", RowBox[List["CosIntegral", "[", RowBox[List["a", " ", "z"]], "]"]]]], SuperscriptBox["b", "3"]], "+", FractionBox[RowBox[List[RowBox[List[RowBox[List["(", RowBox[List[SuperscriptBox["a", "3"], "-", RowBox[List["\[ImaginaryI]", " ", SuperscriptBox["b", "3"]]]]], ")"]], " ", RowBox[List["ExpIntegralEi", "[", RowBox[List[RowBox[List["(", RowBox[List[RowBox[List[RowBox[List["-", "\[ImaginaryI]"]], " ", "a"]], "+", "b"]], ")"]], " ", "z"]], "]"]]]], "+", RowBox[List[RowBox[List["(", RowBox[List[SuperscriptBox["a", "3"], "+", RowBox[List["\[ImaginaryI]", " ", SuperscriptBox["b", "3"]]]]], ")"]], " ", RowBox[List["ExpIntegralEi", "[", RowBox[List[RowBox[List["(", RowBox[List[RowBox[List["\[ImaginaryI]", " ", "a"]], "+", "b"]], ")"]], " ", "z"]], "]"]]]]]], RowBox[List[SuperscriptBox["a", "3"], " ", SuperscriptBox["b", "3"]]]], "+", FractionBox[RowBox[List[SuperscriptBox["\[ExponentialE]", RowBox[List["b", " ", "z"]]], " ", RowBox[List["(", RowBox[List[RowBox[List[SuperscriptBox["a", "2"], " ", RowBox[List["(", RowBox[List[RowBox[List["-", "2"]], "+", RowBox[List["b", " ", "z"]]]], ")"]]]], "+", RowBox[List[SuperscriptBox["b", "2"], " ", RowBox[List["(", RowBox[List["1", "+", RowBox[List["b", " ", "z"]]]], ")"]]]]]], ")"]], " ", RowBox[List["Sin", "[", RowBox[List["a", " ", "z"]], "]"]]]], RowBox[List["a", " ", SuperscriptBox["b", "2"], " ", RowBox[List["(", RowBox[List[SuperscriptBox["a", "2"], "+", SuperscriptBox["b", "2"]]], ")"]]]]], "+", FractionBox[RowBox[List[RowBox[List["ExpIntegralEi", "[", RowBox[List["b", " ", "z"]], "]"]], " ", RowBox[List["(", RowBox[List[RowBox[List[RowBox[List["-", "2"]], " ", "a", " ", "z", " ", RowBox[List["Cos", "[", RowBox[List["a", " ", "z"]], "]"]]]], "+", RowBox[List[SuperscriptBox["a", "3"], " ", SuperscriptBox["z", "3"], " ", RowBox[List["CosIntegral", "[", RowBox[List["a", " ", "z"]], "]"]]]], "+", RowBox[List[RowBox[List["(", RowBox[List["2", "-", RowBox[List[SuperscriptBox["a", "2"], " ", SuperscriptBox["z", "2"]]]]], ")"]], " ", RowBox[List["Sin", "[", RowBox[List["a", " ", "z"]], "]"]]]]]], ")"]]]], SuperscriptBox["a", "3"]]]], ")"]]]]]]]]

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

 2001-10-29