Integrate[(x - 1)/((1 - x y) Log[x y]), {y, 0, 1}, {x, 0, 1}] == EulerGamma

Cell[BoxData[RowBox[List[RowBox[List[SubsuperscriptBox["\[Integral]", "0", "1"], RowBox[List[SubsuperscriptBox["\[Integral]", "0", "1"], RowBox[List[FractionBox[RowBox[List["x", "-", "1"]], RowBox[List[RowBox[List["(", RowBox[List["1", "-", RowBox[List["x", " ", "y"]]]], ")"]], " ", RowBox[List["Log", "[", RowBox[List["x", " ", "y"]], "]"]]]]], RowBox[List["\[DifferentialD]", "x"]], RowBox[List["\[DifferentialD]", "y"]]]]]]]], "\[Equal]", "EulerGamma"]]]]

<math xmlns='http://www.w3.org/1998/Math/MathML' mathematica:form='TraditionalForm' xmlns:mathematica='http://www.wolfram.com/XML/'> <semantics> <mrow> <mrow> <msubsup> <mo> &#8747; </mo> <mn> 0 </mn> <mn> 1 </mn> </msubsup> <mrow> <msubsup> <mo> &#8747; </mo> <mn> 0 </mn> <mn> 1 </mn> </msubsup> <mrow> <mfrac> <mrow> <mi> x </mi> <mo> - </mo> <mn> 1 </mn> </mrow> <mrow> <mrow> <mo> ( </mo> <mrow> <mn> 1 </mn> <mo> - </mo> <mrow> <mi> x </mi> <mo> &#8290; </mo> <mi> y </mi> </mrow> </mrow> <mo> ) </mo> </mrow> <mo> &#8290; </mo> <mrow> <mi> log </mi> <mo> &#8289; </mo> <mo> ( </mo> <mrow> <mi> x </mi> <mo> &#8290; </mo> <mi> y </mi> </mrow> <mo> ) </mo> </mrow> </mrow> </mfrac> <mo> &#8290; </mo> <mrow> <mo> &#8518; </mo> <mi> x </mi> </mrow> <mo> &#8290; </mo> <mrow> <mo> &#8518; </mo> <mi> y </mi> </mrow> </mrow> </mrow> </mrow> <mo> &#63449; </mo> <semantics> <mi> &#8509; </mi> <annotation encoding='Mathematica'> TagBox[&quot;\[DoubledGamma]&quot;, Function[List[], EulerGamma]] </annotation> </semantics> </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> <int /> <bvar> <ci> y </ci> </bvar> <lowlimit> <cn type='integer'> 0 </cn> </lowlimit> <uplimit> <cn type='integer'> 1 </cn> </uplimit> <apply> <times /> <apply> <plus /> <ci> x </ci> <cn type='integer'> -1 </cn> </apply> <apply> <power /> <apply> <times /> <apply> <plus /> <cn type='integer'> 1 </cn> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <ci> x </ci> <ci> y </ci> </apply> </apply> </apply> <apply> <ln /> <apply> <times /> <ci> x </ci> <ci> y </ci> </apply> </apply> </apply> <cn type='integer'> -1 </cn> </apply> </apply> </apply> </apply> <eulergamma /> </apply> </annotation-xml> </semantics> </math>

Cell[BoxData[RowBox[List[RowBox[List["HoldPattern", "[", RowBox[List[SubsuperscriptBox["\[Integral]", "0", "1"], RowBox[List[SubsuperscriptBox["\[Integral]", "0", "1"], RowBox[List[FractionBox[RowBox[List["x_", "-", "1"]], RowBox[List[RowBox[List["(", RowBox[List["1", "-", RowBox[List["x_", " ", "y_"]]]], ")"]], " ", RowBox[List["Log", "[", RowBox[List["x_", " ", "y_"]], "]"]]]]], RowBox[List["\[DifferentialD]", "x_"]], RowBox[List["\[DifferentialD]", "y_"]]]]]]]], "]"]], "\[RuleDelayed]", "EulerGamma"]]]]

2007-05-02