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 Exp

 http://functions.wolfram.com/01.03.21.0417.01

 Input Form

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

 Standard Form

 Cell[BoxData[RowBox[List[RowBox[List["\[Integral]", RowBox[List[SuperscriptBox[RowBox[List["(", SuperscriptBox["\[ExponentialE]", RowBox[List[RowBox[List["b", " ", SqrtBox["z"]]], " ", "+", RowBox[List["d", " ", "z"]]]]], ")"]], "\[Mu]"], " ", SuperscriptBox[RowBox[List["(", SuperscriptBox["\[ExponentialE]", RowBox[List[RowBox[List[SqrtBox["z"], " ", "c"]], "+", RowBox[List["f", " ", "z"]], "+", "g"]]], ")"]], "\[Nu]"], RowBox[List["\[DifferentialD]", "z"]]]]]], "\[Equal]", RowBox[List[FractionBox["1", RowBox[List["2", " ", SuperscriptBox[RowBox[List["(", RowBox[List[RowBox[List["d", " ", "\[Mu]"]], "+", RowBox[List["f", " ", "\[Nu]"]]]], ")"]], RowBox[List["3", "/", "2"]]]]]], RowBox[List["(", RowBox[List[SuperscriptBox["\[ExponentialE]", RowBox[List["-", FractionBox[SuperscriptBox[RowBox[List["(", RowBox[List[RowBox[List["b", " ", "\[Mu]"]], "+", RowBox[List["2", " ", "d", " ", SqrtBox["z"], " ", "\[Mu]"]], "+", RowBox[List[RowBox[List["(", RowBox[List["c", "+", RowBox[List["2", " ", "f", " ", SqrtBox["z"]]]]], ")"]], " ", "\[Nu]"]]]], ")"]], "2"], RowBox[List["4", " ", RowBox[List["(", RowBox[List[RowBox[List["d", " ", "\[Mu]"]], "+", RowBox[List["f", " ", "\[Nu]"]]]], ")"]]]]]]]], " ", SuperscriptBox[RowBox[List["(", SuperscriptBox["\[ExponentialE]", RowBox[List[RowBox[List["b", " ", SqrtBox["z"]]], "+", RowBox[List["d", " ", "z"]]]]], ")"]], "\[Mu]"], " ", SuperscriptBox[RowBox[List["(", SuperscriptBox["\[ExponentialE]", RowBox[List["g", "+", 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["b", " ", "\[Mu]"]], "+", RowBox[List["2", " ", "d", " ", SqrtBox["z"], " ", "\[Mu]"]], "+", RowBox[List["c", " ", "\[Nu]"]], "+", RowBox[List["2", " ", "f", " ", SqrtBox["z"], " ", "\[Nu]"]]]], ")"]], "2"], RowBox[List["4", " ", RowBox[List["(", RowBox[List[RowBox[List["d", " ", "\[Mu]"]], "+", RowBox[List["f", " ", "\[Nu]"]]]], ")"]]]]]], " ", SqrtBox[RowBox[List[RowBox[List["d", " ", "\[Mu]"]], "+", RowBox[List["f", " ", "\[Nu]"]]]]]]], "-", RowBox[List[SqrtBox["\[Pi]"], " ", RowBox[List["(", RowBox[List[RowBox[List["b", " ", "\[Mu]"]], "+", RowBox[List["c", " ", "\[Nu]"]]]], ")"]], " ", RowBox[List["Erfi", "[", FractionBox[RowBox[List[RowBox[List["b", " ", "\[Mu]"]], "+", RowBox[List["2", " ", "d", " ", SqrtBox["z"], " ", "\[Mu]"]], "+", RowBox[List["c", " ", "\[Nu]"]], "+", RowBox[List["2", " ", "f", " ", SqrtBox["z"], " ", "\[Nu]"]]]], RowBox[List["2", " ", SqrtBox[RowBox[List[RowBox[List["d", " ", "\[Mu]"]], "+", RowBox[List["f", " ", "\[Nu]"]]]]]]]], "]"]]]]]], ")"]]]], ")"]]]]]]]]

 MathML Form

 ( z b + d z ) μ ( z c + f z + g ) ν z 1 2 ( d μ + f ν ) 3 / 2 ( - ( b μ + 2 d z μ + ( c + 2 f z ) ν ) 2 4 ( d μ + f ν ) ( z b + d z ) μ ( z c + g + f z ) ν ( 2 ( b μ + 2 d z μ + c ν + 2 f z ν ) 2 4 ( d μ + f ν ) d μ + f ν - π ( b μ + c ν ) erfi ( b μ + 2 d z μ + c ν + 2 f z ν 2 d μ + f ν ) ) ) z z 1 2 b d z μ z 1 2 c f z g ν 1 2 d μ f ν 3 2 -1 -1 b μ 2 d z 1 2 μ c 2 f z 1 2 ν 2 4 d μ f ν -1 z 1 2 b d z μ z 1 2 c g f z ν 2 b μ 2 d z 1 2 μ c ν 2 f z 1 2 ν 2 4 d μ f ν -1 d μ f ν 1 2 -1 1 2 b μ c ν Erfi b μ 2 d z 1 2 μ c ν 2 f z 1 2 ν 2 d μ f ν 1 2 -1 [/itex]

 Rule Form

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

 2002-12-18