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http://functions.wolfram.com/01.03.21.0121.01
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Integrate[(1/z^3) E^(a Sqrt[z]), z] ==
((-E^(a Sqrt[z])) (6 + 2 a Sqrt[z] + a^2 z + a^3 z^(3/2)) +
a^4 z^2 ExpIntegralEi[a Sqrt[z]])/(12 z^2)
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Cell[BoxData[RowBox[List[RowBox[List["\[Integral]", RowBox[List[FractionBox["1", SuperscriptBox["z", "3"]], SuperscriptBox["\[ExponentialE]", RowBox[List["a", " ", SqrtBox["z"]]]], RowBox[List["\[DifferentialD]", "z"]]]]]], "\[Equal]", FractionBox[RowBox[List[RowBox[List[RowBox[List["-", SuperscriptBox["\[ExponentialE]", RowBox[List["a", " ", SqrtBox["z"]]]]]], " ", RowBox[List["(", RowBox[List["6", "+", RowBox[List["2", " ", "a", " ", SqrtBox["z"]]], "+", RowBox[List[SuperscriptBox["a", "2"], " ", "z"]], "+", RowBox[List[SuperscriptBox["a", "3"], " ", SuperscriptBox["z", RowBox[List["3", "/", "2"]]]]]]], ")"]]]], "+", RowBox[List[SuperscriptBox["a", "4"], " ", SuperscriptBox["z", "2"], " ", RowBox[List["ExpIntegralEi", "[", RowBox[List["a", " ", SqrtBox["z"]]], "]"]]]]]], RowBox[List["12", " ", SuperscriptBox["z", "2"]]]]]]]]
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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> <mi> ⅇ </mi> <mrow> <mi> a </mi> <mo> ⁢ </mo> <msqrt> <mi> z </mi> </msqrt> </mrow> </msup> <msup> <mi> z </mi> <mn> 3 </mn> </msup> </mfrac> <mo> ⁢ </mo> <mrow> <mo> ⅆ </mo> <mi> z </mi> </mrow> </mrow> </mrow> <mo> ⩵ </mo> <mfrac> <mrow> <mrow> <msup> <mi> a </mi> <mn> 4 </mn> </msup> <mo> ⁢ </mo> <msup> <mi> z </mi> <mn> 2 </mn> </msup> <mo> ⁢ </mo> <mrow> <mi> Ei </mi> <mo> ⁡ </mo> <mo> ( </mo> <mrow> <mi> a </mi> <mo> ⁢ </mo> <msqrt> <mi> z </mi> </msqrt> </mrow> <mo> ) </mo> </mrow> </mrow> <mo> - </mo> <mrow> <msup> <mi> ⅇ </mi> <mrow> <mi> a </mi> <mo> ⁢ </mo> <msqrt> <mi> z </mi> </msqrt> </mrow> </msup> <mo> ⁢ </mo> <mrow> <mo> ( </mo> <mrow> <mrow> <msup> <mi> a </mi> <mn> 3 </mn> </msup> <mo> ⁢ </mo> <msup> <mi> z </mi> <mrow> <mn> 3 </mn> <mo> / </mo> <mn> 2 </mn> </mrow> </msup> </mrow> <mo> + </mo> <mrow> <msup> <mi> a </mi> <mn> 2 </mn> </msup> <mo> ⁢ </mo> <mi> z </mi> </mrow> <mo> + </mo> <mrow> <mn> 2 </mn> <mo> ⁢ </mo> <mi> a </mi> <mo> ⁢ </mo> <msqrt> <mi> z </mi> </msqrt> </mrow> <mo> + </mo> <mn> 6 </mn> </mrow> <mo> ) </mo> </mrow> </mrow> </mrow> <mrow> <mn> 12 </mn> <mo> ⁢ </mo> <msup> <mi> z </mi> <mn> 2 </mn> </msup> </mrow> </mfrac> </mrow> <annotation-xml encoding='MathML-Content'> <apply> <eq /> <apply> <int /> <bvar> <ci> z </ci> </bvar> <apply> <times /> <apply> <power /> <exponentiale /> <apply> <times /> <ci> a </ci> <apply> <power /> <ci> z </ci> <cn type='rational'> 1 <sep /> 2 </cn> </apply> </apply> </apply> <apply> <power /> <apply> <power /> <ci> z </ci> <cn type='integer'> 3 </cn> </apply> <cn type='integer'> -1 </cn> </apply> </apply> </apply> <apply> <times /> <apply> <plus /> <apply> <times /> <apply> <power /> <ci> a </ci> <cn type='integer'> 4 </cn> </apply> <apply> <power /> <ci> z </ci> <cn type='integer'> 2 </cn> </apply> <apply> <ci> ExpIntegralEi </ci> <apply> <times /> <ci> a </ci> <apply> <power /> <ci> z </ci> <cn type='rational'> 1 <sep /> 2 </cn> </apply> </apply> </apply> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <apply> <power /> <exponentiale /> <apply> <times /> <ci> a </ci> <apply> <power /> <ci> z </ci> <cn type='rational'> 1 <sep /> 2 </cn> </apply> </apply> </apply> <apply> <plus /> <apply> <times /> <apply> <power /> <ci> a </ci> <cn type='integer'> 3 </cn> </apply> <apply> <power /> <ci> z </ci> <cn type='rational'> 3 <sep /> 2 </cn> </apply> </apply> <apply> <times /> <apply> <power /> <ci> a </ci> <cn type='integer'> 2 </cn> </apply> <ci> z </ci> </apply> <apply> <times /> <cn type='integer'> 2 </cn> <ci> a </ci> <apply> <power /> <ci> z </ci> <cn type='rational'> 1 <sep /> 2 </cn> </apply> </apply> <cn type='integer'> 6 </cn> </apply> </apply> </apply> </apply> <apply> <power /> <apply> <times /> <cn type='integer'> 12 </cn> <apply> <power /> <ci> z </ci> <cn type='integer'> 2 </cn> </apply> </apply> <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["\[ExponentialE]", RowBox[List["a_", " ", SqrtBox["z_"]]]], SuperscriptBox["z_", "3"]], RowBox[List["\[DifferentialD]", "z_"]]]]]], "]"]], "\[RuleDelayed]", FractionBox[RowBox[List[RowBox[List[RowBox[List["-", SuperscriptBox["\[ExponentialE]", RowBox[List["a", " ", SqrtBox["z"]]]]]], " ", RowBox[List["(", RowBox[List["6", "+", RowBox[List["2", " ", "a", " ", SqrtBox["z"]]], "+", RowBox[List[SuperscriptBox["a", "2"], " ", "z"]], "+", RowBox[List[SuperscriptBox["a", "3"], " ", SuperscriptBox["z", RowBox[List["3", "/", "2"]]]]]]], ")"]]]], "+", RowBox[List[SuperscriptBox["a", "4"], " ", SuperscriptBox["z", "2"], " ", RowBox[List["ExpIntegralEi", "[", RowBox[List["a", " ", SqrtBox["z"]]], "]"]]]]]], RowBox[List["12", " ", SuperscriptBox["z", "2"]]]]]]]] |
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Date Added to functions.wolfram.com (modification date)
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