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ExpIntegralEi






Mathematica Notation

Traditional Notation









Gamma, Beta, Erf > ExpIntegralEi[z] > Integration > Indefinite integration > Involving functions of the direct function and elementary functions > Involving elementary functions of the direct function and elementary functions > Involving products of the direct function and a power function





http://functions.wolfram.com/06.35.21.0067.01









  


  










Input Form





Integrate[z^2 ExpIntegralEi[a z] ExpIntegralEi[b z], z] == (1/(3 a^3 b^3 (a + b))) (a b E^((a + b) z) (-2 a^2 - a b - 2 b^2 + a b (a + b) z) + (a + b) ((-b^3) E^(a z) (2 + a z (-2 + a z)) ExpIntegralEi[b z] + a^3 ExpIntegralEi[a z] ((-E^(b z)) (2 + b z (-2 + b z)) + b^3 z^3 ExpIntegralEi[b z]) + 2 (a^3 + b^3) ExpIntegralEi[(a + b) 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[SuperscriptBox["z_", "2"], " ", RowBox[List["ExpIntegralEi", "[", RowBox[List["a_", " ", "z_"]], "]"]], " ", RowBox[List["ExpIntegralEi", "[", RowBox[List["b_", " ", "z_"]], "]"]]]], RowBox[List["\[DifferentialD]", "z_"]]]]]], "]"]], "\[RuleDelayed]", FractionBox[RowBox[List[RowBox[List["a", " ", "b", " ", SuperscriptBox["\[ExponentialE]", RowBox[List[RowBox[List["(", RowBox[List["a", "+", "b"]], ")"]], " ", "z"]]], " ", RowBox[List["(", RowBox[List[RowBox[List[RowBox[List["-", "2"]], " ", SuperscriptBox["a", "2"]]], "-", RowBox[List["a", " ", "b"]], "-", RowBox[List["2", " ", SuperscriptBox["b", "2"]]], "+", RowBox[List["a", " ", "b", " ", RowBox[List["(", RowBox[List["a", "+", "b"]], ")"]], " ", "z"]]]], ")"]]]], "+", RowBox[List[RowBox[List["(", RowBox[List["a", "+", "b"]], ")"]], " ", RowBox[List["(", RowBox[List[RowBox[List[RowBox[List["-", SuperscriptBox["b", "3"]]], " ", SuperscriptBox["\[ExponentialE]", RowBox[List["a", " ", "z"]]], " ", RowBox[List["(", RowBox[List["2", "+", RowBox[List["a", " ", "z", " ", RowBox[List["(", RowBox[List[RowBox[List["-", "2"]], "+", RowBox[List["a", " ", "z"]]]], ")"]]]]]], ")"]], " ", RowBox[List["ExpIntegralEi", "[", RowBox[List["b", " ", "z"]], "]"]]]], "+", RowBox[List[SuperscriptBox["a", "3"], " ", RowBox[List["ExpIntegralEi", "[", RowBox[List["a", " ", "z"]], "]"]], " ", RowBox[List["(", RowBox[List[RowBox[List[RowBox[List["-", SuperscriptBox["\[ExponentialE]", RowBox[List["b", " ", "z"]]]]], " ", RowBox[List["(", RowBox[List["2", "+", RowBox[List["b", " ", "z", " ", RowBox[List["(", RowBox[List[RowBox[List["-", "2"]], "+", RowBox[List["b", " ", "z"]]]], ")"]]]]]], ")"]]]], "+", RowBox[List[SuperscriptBox["b", "3"], " ", SuperscriptBox["z", "3"], " ", RowBox[List["ExpIntegralEi", "[", RowBox[List["b", " ", "z"]], "]"]]]]]], ")"]]]], "+", RowBox[List["2", " ", RowBox[List["(", RowBox[List[SuperscriptBox["a", "3"], "+", SuperscriptBox["b", "3"]]], ")"]], " ", RowBox[List["ExpIntegralEi", "[", RowBox[List[RowBox[List["(", RowBox[List["a", "+", "b"]], ")"]], " ", "z"]], "]"]]]]]], ")"]]]]]], RowBox[List["3", " ", SuperscriptBox["a", "3"], " ", SuperscriptBox["b", "3"], " ", RowBox[List["(", RowBox[List["a", "+", "b"]], ")"]]]]]]]]]










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





2001-10-29





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