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 Exp

 http://functions.wolfram.com/01.03.21.0105.01

 Input Form

 Integrate[z^3 E^(a z^2), z] == (1/2) E^(a z^2) (-(1/a^2) + z^2/a)

 Standard Form

 Cell[BoxData[RowBox[List[RowBox[List["\[Integral]", RowBox[List[SuperscriptBox["z", "3"], " ", SuperscriptBox["\[ExponentialE]", RowBox[List["a", " ", SuperscriptBox["z", "2"]]]], RowBox[List["\[DifferentialD]", "z"]]]]]], "\[Equal]", RowBox[List[FractionBox["1", "2"], " ", SuperscriptBox["\[ExponentialE]", RowBox[List["a", " ", SuperscriptBox["z", "2"]]]], " ", RowBox[List["(", RowBox[List[RowBox[List["-", FractionBox["1", SuperscriptBox["a", "2"]]]], "+", FractionBox[SuperscriptBox["z", "2"], "a"]]], ")"]]]]]]]]

 MathML Form

 z 3 a z 2 z 1 2 a z 2 ( z 2 a - 1 a 2 ) z z 3 a z 2 1 2 a z 2 z 2 a -1 -1 1 a 2 -1 [/itex]

 Rule Form

 Cell[BoxData[RowBox[List[RowBox[List["HoldPattern", "[", RowBox[List["\[Integral]", RowBox[List[RowBox[List[SuperscriptBox["z_", "3"], " ", SuperscriptBox["\[ExponentialE]", RowBox[List["a_", " ", SuperscriptBox["z_", "2"]]]]]], RowBox[List["\[DifferentialD]", "z_"]]]]]], "]"]], "\[RuleDelayed]", RowBox[List[FractionBox["1", "2"], " ", SuperscriptBox["\[ExponentialE]", RowBox[List["a", " ", SuperscriptBox["z", "2"]]]], " ", RowBox[List["(", RowBox[List[RowBox[List["-", FractionBox["1", SuperscriptBox["a", "2"]]]], "+", FractionBox[SuperscriptBox["z", "2"], "a"]]], ")"]]]]]]]]

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

 2002-12-18