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 Log

 http://functions.wolfram.com/01.04.21.0071.01

 Input Form

 Integrate[t^2 Log[2 Sin[t/2]]^2, {t, 0, 2 Pi}] == (13 Pi^5)/45

 Standard Form

 Cell[BoxData[RowBox[List[RowBox[List[SubsuperscriptBox["\[Integral]", "0", RowBox[List["2", " ", "\[Pi]"]]], RowBox[List[RowBox[List[SuperscriptBox["t", "2"], " ", SuperscriptBox[RowBox[List["Log", "[", RowBox[List["2", " ", RowBox[List["Sin", "[", FractionBox["t", "2"], "]"]]]], "]"]], "2"]]], RowBox[List["\[DifferentialD]", "t"]]]]]], "\[Equal]", FractionBox[RowBox[List["13", " ", SuperscriptBox["\[Pi]", "5"]]], "45"]]]]]

 MathML Form

 0 2 π t 2 log 2 ( 2 sin ( t 2 ) ) t 13 π 5 45 t 0 2 t 2 2 t 2 -1 2 13 5 45 -1 [/itex]

 Rule Form

 Cell[BoxData[RowBox[List[RowBox[List["HoldPattern", "[", RowBox[List[SubsuperscriptBox["\[Integral]", "0", RowBox[List["2", " ", "\[Pi]"]]], RowBox[List[RowBox[List[SuperscriptBox["t_", "2"], " ", SuperscriptBox[RowBox[List["Log", "[", RowBox[List["2", " ", RowBox[List["Sin", "[", FractionBox["t_", "2"], "]"]]]], "]"]], "2"]]], RowBox[List["\[DifferentialD]", "t_"]]]]]], "]"]], "\[RuleDelayed]", FractionBox[RowBox[List["13", " ", SuperscriptBox["\[Pi]", "5"]]], "45"]]]]]

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

 2001-10-29