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 Log

 http://functions.wolfram.com/01.04.21.0052.01

 Input Form

 Integrate[Log[2 Sin[t/2]]^6, {t, 0, Pi}] == (275 Pi^7)/1344 + (45/2) Pi Zeta[3]^2

 Standard Form

 Cell[BoxData[RowBox[List[RowBox[List[SubsuperscriptBox["\[Integral]", "0", "\[Pi]"], RowBox[List[SuperscriptBox[RowBox[List["Log", "[", RowBox[List["2", " ", RowBox[List["Sin", "[", FractionBox["t", "2"], "]"]]]], "]"]], "6"], RowBox[List["\[DifferentialD]", "t"]]]]]], "\[Equal]", RowBox[List[FractionBox[RowBox[List["275", " ", SuperscriptBox["\[Pi]", "7"]]], "1344"], "+", RowBox[List[FractionBox["45", "2"], " ", "\[Pi]", " ", SuperscriptBox[RowBox[List["Zeta", "[", "3", "]"]], "2"]]]]]]]]]

 MathML Form

 0 π log 6 ( 2 sin ( t 2 ) ) t 45 2 π ζ ( 3 ) TagBox[RowBox[List["\[Zeta]", "(", TagBox["3", Rule[Editable, True]], ")"]], InterpretTemplate[Function[BoxForm`e\$, Zeta[BoxForm`e\$]]]] 2 + 275 π 7 1344 t 0 2 t 2 -1 6 45 2 Zeta 3 2 275 7 1344 -1 [/itex]

 Rule Form

 Cell[BoxData[RowBox[List[RowBox[List["HoldPattern", "[", RowBox[List[SubsuperscriptBox["\[Integral]", "0", "\[Pi]"], RowBox[List[SuperscriptBox[RowBox[List["Log", "[", RowBox[List["2", " ", RowBox[List["Sin", "[", FractionBox["t_", "2"], "]"]]]], "]"]], "6"], RowBox[List["\[DifferentialD]", "t_"]]]]]], "]"]], "\[RuleDelayed]", RowBox[List[FractionBox[RowBox[List["275", " ", SuperscriptBox["\[Pi]", "7"]]], "1344"], "+", RowBox[List[FractionBox["45", "2"], " ", "\[Pi]", " ", SuperscriptBox[RowBox[List["Zeta", "[", "3", "]"]], "2"]]]]]]]]]

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

 2001-10-29