html, body, form { margin: 0; padding: 0; width: 100%; } #calculate { position: relative; width: 177px; height: 110px; background: transparent url(/images/alphabox/embed_functions_inside.gif) no-repeat scroll 0 0; } #i { position: relative; left: 18px; top: 44px; width: 133px; border: 0 none; outline: 0; font-size: 11px; } #eq { width: 9px; height: 10px; background: transparent; position: absolute; top: 47px; right: 18px; cursor: pointer; }

 ArcTanh

 http://functions.wolfram.com/01.27.21.0002.01

 Input Form

 Integrate[ArcTanh[z]/z, z] == (1/2) (PolyLog[2, z] - PolyLog[2, -z])

 Standard Form

 Cell[BoxData[RowBox[List[RowBox[List["\[Integral]", RowBox[List[FractionBox[RowBox[List["ArcTanh", "[", "z", "]"]], "z"], RowBox[List["\[DifferentialD]", "z"]]]]]], "\[Equal]", RowBox[List[FractionBox["1", "2"], RowBox[List["(", RowBox[List[RowBox[List["PolyLog", "[", RowBox[List["2", ",", "z"]], "]"]], "-", RowBox[List["PolyLog", "[", RowBox[List["2", ",", RowBox[List["-", "z"]]]], "]"]]]], ")"]]]]]]]]

 MathML Form

 tanh - 1 ( z ) z z 1 2 ( Li PolyLog 2 ( z ) - Li PolyLog 2 ( - z ) ) z z z -1 1 2 PolyLog 2 z -1 PolyLog 2 -1 z [/itex]

 Rule Form

 Cell[BoxData[RowBox[List[RowBox[List["HoldPattern", "[", RowBox[List["\[Integral]", RowBox[List[FractionBox[RowBox[List["ArcTanh", "[", "z_", "]"]], "z_"], RowBox[List["\[DifferentialD]", "z_"]]]]]], "]"]], "\[RuleDelayed]", RowBox[List[FractionBox["1", "2"], " ", RowBox[List["(", RowBox[List[RowBox[List["PolyLog", "[", RowBox[List["2", ",", "z"]], "]"]], "-", RowBox[List["PolyLog", "[", RowBox[List["2", ",", RowBox[List["-", "z"]]]], "]"]]]], ")"]]]]]]]]

 Date Added to functions.wolfram.com (modification date)

 2001-10-29