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http://functions.wolfram.com/01.03.21.0540.01
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Integrate[(1/z) (E^(a z^r))^\[Nu], z] ==
((E^(a z^r))^\[Nu] ExpIntegralEi[a z^r \[Nu]])/(E^(a z^r \[Nu]) r)
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Cell[BoxData[RowBox[List[RowBox[List["\[Integral]", RowBox[List[FractionBox["1", "z"], SuperscriptBox[RowBox[List["(", SuperscriptBox["\[ExponentialE]", RowBox[List["a", " ", SuperscriptBox["z", "r"]]]], ")"]], "\[Nu]"], " ", RowBox[List["\[DifferentialD]", "z"]]]]]], "\[Equal]", FractionBox[RowBox[List[SuperscriptBox["\[ExponentialE]", RowBox[List[RowBox[List["-", "a"]], " ", SuperscriptBox["z", "r"], " ", "\[Nu]"]]], " ", SuperscriptBox[RowBox[List["(", SuperscriptBox["\[ExponentialE]", RowBox[List["a", " ", SuperscriptBox["z", "r"]]]], ")"]], "\[Nu]"], " ", RowBox[List["ExpIntegralEi", "[", RowBox[List["a", " ", SuperscriptBox["z", "r"], " ", "\[Nu]"]], "]"]]]], "r"]]]]]
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<math xmlns='http://www.w3.org/1998/Math/MathML' mathematica:form='TraditionalForm' xmlns:mathematica='http://www.wolfram.com/XML/'> <semantics> <mrow> <mrow> <mo> ∫ </mo> <mrow> <mfrac> <msup> <mrow> <mo> ( </mo> <msup> <mi> ⅇ </mi> <mrow> <mi> a </mi> <mo> ⁢ </mo> <msup> <mi> z </mi> <mi> r </mi> </msup> </mrow> </msup> <mo> ) </mo> </mrow> <mi> ν </mi> </msup> <mi> z </mi> </mfrac> <mo> ⁢ </mo> <mrow> <mo> ⅆ </mo> <mi> z </mi> </mrow> </mrow> </mrow> <mo> ⩵ </mo> <mfrac> <mrow> <msup> <mi> ⅇ </mi> <mrow> <mrow> <mo> - </mo> <mi> a </mi> </mrow> <mo> ⁢ </mo> <msup> <mi> z </mi> <mi> r </mi> </msup> <mo> ⁢ </mo> <mi> ν </mi> </mrow> </msup> <mo> ⁢ </mo> <msup> <mrow> <mo> ( </mo> <msup> <mi> ⅇ </mi> <mrow> <mi> a </mi> <mo> ⁢ </mo> <msup> <mi> z </mi> <mi> r </mi> </msup> </mrow> </msup> <mo> ) </mo> </mrow> <mi> ν </mi> </msup> <mo> ⁢ </mo> <mrow> <mi> Ei </mi> <mo> ⁡ </mo> <mo> ( </mo> <mrow> <mi> a </mi> <mo> ⁢ </mo> <msup> <mi> z </mi> <mi> r </mi> </msup> <mo> ⁢ </mo> <mi> ν </mi> </mrow> <mo> ) </mo> </mrow> </mrow> <mi> r </mi> </mfrac> </mrow> <annotation-xml encoding='MathML-Content'> <apply> <eq /> <apply> <int /> <bvar> <ci> z </ci> </bvar> <apply> <times /> <apply> <power /> <apply> <power /> <exponentiale /> <apply> <times /> <ci> a </ci> <apply> <power /> <ci> z </ci> <ci> r </ci> </apply> </apply> </apply> <ci> ν </ci> </apply> <apply> <power /> <ci> z </ci> <cn type='integer'> -1 </cn> </apply> </apply> </apply> <apply> <times /> <apply> <power /> <exponentiale /> <apply> <times /> <apply> <times /> <cn type='integer'> -1 </cn> <ci> a </ci> </apply> <apply> <power /> <ci> z </ci> <ci> r </ci> </apply> <ci> ν </ci> </apply> </apply> <apply> <power /> <apply> <power /> <exponentiale /> <apply> <times /> <ci> a </ci> <apply> <power /> <ci> z </ci> <ci> r </ci> </apply> </apply> </apply> <ci> ν </ci> </apply> <apply> <ci> ExpIntegralEi </ci> <apply> <times /> <ci> a </ci> <apply> <power /> <ci> z </ci> <ci> r </ci> </apply> <ci> ν </ci> </apply> </apply> <apply> <power /> <ci> r </ci> <cn type='integer'> -1 </cn> </apply> </apply> </apply> </annotation-xml> </semantics> </math>
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| Cell[BoxData[RowBox[List[RowBox[List["HoldPattern", "[", RowBox[List["\[Integral]", RowBox[List[FractionBox[SuperscriptBox[RowBox[List["(", SuperscriptBox["\[ExponentialE]", RowBox[List["a_", " ", SuperscriptBox["z_", "r_"]]]], ")"]], "\[Nu]_"], "z_"], RowBox[List["\[DifferentialD]", "z_"]]]]]], "]"]], "\[RuleDelayed]", FractionBox[RowBox[List[SuperscriptBox["\[ExponentialE]", RowBox[List[RowBox[List["-", "a"]], " ", SuperscriptBox["z", "r"], " ", "\[Nu]"]]], " ", SuperscriptBox[RowBox[List["(", SuperscriptBox["\[ExponentialE]", RowBox[List["a", " ", SuperscriptBox["z", "r"]]]], ")"]], "\[Nu]"], " ", RowBox[List["ExpIntegralEi", "[", RowBox[List["a", " ", SuperscriptBox["z", "r"], " ", "\[Nu]"]], "]"]]]], "r"]]]]] |
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Date Added to functions.wolfram.com (modification date)
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){kind=small}
