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ExpIntegralEi






Mathematica Notation

Traditional Notation









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





http://functions.wolfram.com/06.35.21.0019.01









  


  










Input Form





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










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





2001-10-29





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