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 ArcCot

 http://functions.wolfram.com/01.16.21.0013.01

 Input Form

 Integrate[Log[t] ArcCot[t], {t, 0, 1}] == (-(1/48)) (Pi^2 + 24 Log[2] + 12 Pi)

 Standard Form

 Cell[BoxData[RowBox[List[RowBox[List[SubsuperscriptBox["\[Integral]", "0", "1"], RowBox[List[RowBox[List["Log", "[", "t", "]"]], " ", RowBox[List["ArcCot", "[", "t", "]"]], RowBox[List["\[DifferentialD]", "t"]]]]]], "\[Equal]", RowBox[List[RowBox[List["-", FractionBox["1", "48"]]], " ", RowBox[List["(", RowBox[List[SuperscriptBox["\[Pi]", "2"], "+", RowBox[List["24", " ", RowBox[List["Log", "[", "2", "]"]]]], "+", RowBox[List["12", " ", "\[Pi]"]]]], ")"]]]]]]]]

 MathML Form

 0 1 log ( t ) cot - 1 ( t ) t - 1 48 ( π 2 + 24 Log [ 2 ] + 12 π ) t 0 1 t t -1 1 48 2 24 2 12 [/itex]

 Rule Form

 Cell[BoxData[RowBox[List[RowBox[List["HoldPattern", "[", RowBox[List[SubsuperscriptBox["\[Integral]", "0", "1"], RowBox[List[RowBox[List[RowBox[List["Log", "[", "t_", "]"]], " ", RowBox[List["ArcCot", "[", "t_", "]"]]]], RowBox[List["\[DifferentialD]", "t_"]]]]]], "]"]], "\[RuleDelayed]", RowBox[List[RowBox[List["-", FractionBox["1", "48"]]], " ", RowBox[List["(", RowBox[List[SuperscriptBox["\[Pi]", "2"], "+", RowBox[List["24", " ", RowBox[List["Log", "[", "2", "]"]]]], "+", RowBox[List["12", " ", "\[Pi]"]]]], ")"]]]]]]]]

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

 2001-10-29