Integrate[ArcTanh[t]/t, {t, 0, 1}] == Pi^2/8

Cell[BoxData[RowBox[List[RowBox[List[SubsuperscriptBox["\[Integral]", "0", "1"], RowBox[List[FractionBox[RowBox[List["ArcTanh", "[", "t", "]"]], "t"], RowBox[List["\[DifferentialD]", "t"]]]]]], "\[Equal]", FractionBox[SuperscriptBox["\[Pi]", "2"], "8"]]]]]

<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> <mfrac> <mrow> <msup> <mi> tanh </mi> <mrow> <mo> - </mo> <mn> 1 </mn> </mrow> </msup> <mo> ( </mo> <mi> t </mi> <mo> ) </mo> </mrow> <mi> t </mi> </mfrac> <mo> &#8290; </mo> <mrow> <mo> &#8518; </mo> <mi> t </mi> </mrow> </mrow> </mrow> <mo> &#10869; </mo> <mfrac> <msup> <mi> &#960; </mi> <mn> 2 </mn> </msup> <mn> 8 </mn> </mfrac> </mrow> <annotation-xml encoding='MathML-Content'> <apply> <eq /> <apply> <int /> <bvar> <ci> t </ci> </bvar> <lowlimit> <cn type='integer'> 0 </cn> </lowlimit> <uplimit> <cn type='integer'> 1 </cn> </uplimit> <apply> <times /> <apply> <arctanh /> <ci> t </ci> </apply> <apply> <power /> <ci> t </ci> <cn type='integer'> -1 </cn> </apply> </apply> </apply> <apply> <times /> <apply> <power /> <pi /> <cn type='integer'> 2 </cn> </apply> <apply> <power /> <cn type='integer'> 8 </cn> <cn type='integer'> -1 </cn> </apply> </apply> </apply> </annotation-xml> </semantics> </math>

Cell[BoxData[RowBox[List[RowBox[List["HoldPattern", "[", RowBox[List[SubsuperscriptBox["\[Integral]", "0", "1"], RowBox[List[FractionBox[RowBox[List["ArcTanh", "[", "t_", "]"]], "t_"], RowBox[List["\[DifferentialD]", "t_"]]]]]], "]"]], "\[RuleDelayed]", FractionBox[SuperscriptBox["\[Pi]", "2"], "8"]]]]]

2001-10-29