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http://functions.wolfram.com/01.31.21.0004.01
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Integrate[-(Log[E^ProductLog[x Log[x]]]/x), {x, 0, 1}] == Pi^2/6
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Cell[BoxData[RowBox[List[RowBox[List[SubsuperscriptBox["\[Integral]", "0", "1"], RowBox[List[RowBox[List["-", FractionBox[RowBox[List["Log", "[", SuperscriptBox["\[ExponentialE]", RowBox[List["ProductLog", "[", RowBox[List["x", " ", RowBox[List["Log", "[", "x", "]"]]]], "]"]]], "]"]], "x"]]], RowBox[List["\[DifferentialD]", "x"]]]]]], "\[Equal]", FractionBox[SuperscriptBox["\[Pi]", "2"], "6"]]]]]
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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> <msubsup> <mo> ∫ </mo> <mn> 0 </mn> <mn> 1 </mn> </msubsup> <mrow> <mrow> <mo> - </mo> <mfrac> <mrow> <mi> log </mi> <mo> ⁡ </mo> <mo> ( </mo> <msup> <mi> ⅇ </mi> <mrow> <mi> W </mi> <mo> [ </mo> <mrow> <mi> x </mi> <mo> ⁢ </mo> <mrow> <mi> log </mi> <mo> ⁡ </mo> <mo> ( </mo> <mi> x </mi> <mo> ) </mo> </mrow> </mrow> <mo> ] </mo> </mrow> </msup> <mo> ) </mo> </mrow> <mi> x </mi> </mfrac> </mrow> <mo> ⁢ </mo> <mrow> <mo> ⅆ </mo> <mi> x </mi> </mrow> </mrow> </mrow> <mo> ⩵ </mo> <mfrac> <msup> <mi> π </mi> <mn> 2 </mn> </msup> <mn> 6 </mn> </mfrac> </mrow> <annotation-xml encoding='MathML-Content'> <apply> <eq /> <apply> <int /> <bvar> <ci> x </ci> </bvar> <lowlimit> <cn type='integer'> 0 </cn> </lowlimit> <uplimit> <cn type='integer'> 1 </cn> </uplimit> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <apply> <ln /> <apply> <power /> <exponentiale /> <apply> <ci> W </ci> <apply> <times /> <ci> x </ci> <apply> <ln /> <ci> x </ci> </apply> </apply> </apply> </apply> </apply> <apply> <power /> <ci> x </ci> <cn type='integer'> -1 </cn> </apply> </apply> </apply> </apply> <apply> <times /> <apply> <power /> <pi /> <cn type='integer'> 2 </cn> </apply> <apply> <power /> <cn type='integer'> 6 </cn> <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[SubsuperscriptBox["\[Integral]", "0", "1"], RowBox[List[RowBox[List["-", FractionBox[RowBox[List["Log", "[", SuperscriptBox["\[ExponentialE]", RowBox[List["ProductLog", "[", RowBox[List["x_", " ", RowBox[List["Log", "[", "x_", "]"]]]], "]"]]], "]"]], "x_"]]], RowBox[List["\[DifferentialD]", "x_"]]]]]], "]"]], "\[RuleDelayed]", FractionBox[SuperscriptBox["\[Pi]", "2"], "6"]]]]] |
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Date Added to functions.wolfram.com (modification date)
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