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Exp




Mathematica Notation

Traditional Notation









Elementary Functions > Exp[z] > Integration > Indefinite integration > Involving functions of the direct function > Involving products of powers of the direct function > Involving product of power of the direct function and the direct function > Involving ed z (ec zr+f z)nu





http://functions.wolfram.com/01.03.21.0355.01









  


  








Input Form





Integrate[E^(d z) (E^(Sqrt[z] c + f z))^\[Nu], z] == (1/(2 (d + f \[Nu])^(3/2))) (E^(d z - (2 d Sqrt[z] + (c + 2 f Sqrt[z]) \[Nu])^2/(4 (d + f \[Nu]))) (E^(c Sqrt[z] + f z))^\[Nu] (2 E^((2 d Sqrt[z] + c \[Nu] + 2 f Sqrt[z] \[Nu])^2/(4 (d + f \[Nu]))) Sqrt[d + f \[Nu]] - c Sqrt[Pi] \[Nu] Erfi[(2 d Sqrt[z] + c \[Nu] + 2 f Sqrt[z] \[Nu])/(2 Sqrt[d + f \[Nu]])]))








Standard Form





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MathML Form







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</ci> </apply> </apply> </apply> <cn type='integer'> -1 </cn> </apply> </apply> </apply> </apply> </apply> <apply> <power /> <apply> <power /> <exponentiale /> <apply> <plus /> <apply> <times /> <apply> <power /> <ci> z </ci> <cn type='rational'> 1 <sep /> 2 </cn> </apply> <ci> c </ci> </apply> <apply> <times /> <ci> f </ci> <ci> z </ci> </apply> </apply> </apply> <ci> &#957; </ci> </apply> <apply> <plus /> <apply> <times /> <cn type='integer'> 2 </cn> <apply> <power /> <exponentiale /> <apply> <times /> <apply> <power /> <apply> <plus /> <apply> <times /> <cn type='integer'> 2 </cn> <apply> <power /> <ci> z </ci> <cn type='rational'> 1 <sep /> 2 </cn> </apply> <ci> d </ci> </apply> <apply> <times /> <ci> c </ci> <ci> &#957; </ci> </apply> <apply> <times /> <cn type='integer'> 2 </cn> <ci> f </ci> <apply> <power /> <ci> z </ci> <cn type='rational'> 1 <sep /> 2 </cn> </apply> <ci> &#957; </ci> </apply> </apply> <cn type='integer'> 2 </cn> </apply> <apply> <power /> <apply> <times /> <cn type='integer'> 4 </cn> <apply> <plus /> <ci> d </ci> <apply> <times /> <ci> f </ci> <ci> &#957; 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Rule Form





Cell[BoxData[RowBox[List[RowBox[List["HoldPattern", "[", RowBox[List["\[Integral]", RowBox[List[RowBox[List[SuperscriptBox["\[ExponentialE]", RowBox[List["d_", " ", "z_"]]], " ", SuperscriptBox[RowBox[List["(", SuperscriptBox["\[ExponentialE]", RowBox[List[RowBox[List[SqrtBox["z_"], " ", "c_"]], "+", RowBox[List["f_", " ", "z_"]]]]], ")"]], "\[Nu]_"]]], RowBox[List["\[DifferentialD]", "z_"]]]]]], "]"]], "\[RuleDelayed]", FractionBox[RowBox[List[SuperscriptBox["\[ExponentialE]", RowBox[List[RowBox[List["d", " ", "z"]], "-", FractionBox[SuperscriptBox[RowBox[List["(", RowBox[List[RowBox[List["2", " ", "d", " ", SqrtBox["z"]]], "+", RowBox[List[RowBox[List["(", RowBox[List["c", "+", RowBox[List["2", " ", "f", " ", SqrtBox["z"]]]]], ")"]], " ", "\[Nu]"]]]], ")"]], "2"], RowBox[List["4", " ", RowBox[List["(", RowBox[List["d", "+", RowBox[List["f", " ", "\[Nu]"]]]], ")"]]]]]]]], " ", SuperscriptBox[RowBox[List["(", SuperscriptBox["\[ExponentialE]", RowBox[List[RowBox[List["c", " ", SqrtBox["z"]]], "+", RowBox[List["f", " ", "z"]]]]], ")"]], "\[Nu]"], " ", RowBox[List["(", RowBox[List[RowBox[List["2", " ", SuperscriptBox["\[ExponentialE]", FractionBox[SuperscriptBox[RowBox[List["(", RowBox[List[RowBox[List["2", " ", "d", " ", SqrtBox["z"]]], "+", RowBox[List["c", " ", "\[Nu]"]], "+", RowBox[List["2", " ", "f", " ", SqrtBox["z"], " ", "\[Nu]"]]]], ")"]], "2"], RowBox[List["4", " ", RowBox[List["(", RowBox[List["d", "+", RowBox[List["f", " ", "\[Nu]"]]]], ")"]]]]]], " ", SqrtBox[RowBox[List["d", "+", RowBox[List["f", " ", "\[Nu]"]]]]]]], "-", RowBox[List["c", " ", SqrtBox["\[Pi]"], " ", "\[Nu]", " ", RowBox[List["Erfi", "[", FractionBox[RowBox[List[RowBox[List["2", " ", "d", " ", SqrtBox["z"]]], "+", RowBox[List["c", " ", "\[Nu]"]], "+", RowBox[List["2", " ", "f", " ", SqrtBox["z"], " ", "\[Nu]"]]]], RowBox[List["2", " ", SqrtBox[RowBox[List["d", "+", RowBox[List["f", " ", "\[Nu]"]]]]]]]], "]"]]]]]], ")"]]]], RowBox[List["2", " ", SuperscriptBox[RowBox[List["(", RowBox[List["d", "+", RowBox[List["f", " ", "\[Nu]"]]]], ")"]], RowBox[List["3", "/", "2"]]]]]]]]]]


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





2002-12-18