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 Power

 http://functions.wolfram.com/01.02.21.0008.01

 Input Form

 Integrate[t^a Log[t], {t, 0, 1}] == -(1/(1 + a)^2) /; Re[a] > -1

 Standard Form

 Cell[BoxData[RowBox[List[RowBox[List[RowBox[List[SubsuperscriptBox["\[Integral]", "0", "1"], RowBox[List[SuperscriptBox["t", "a"], RowBox[List["Log", "[", "t", "]"]], RowBox[List["\[DifferentialD]", "t"]]]]]], "\[Equal]", RowBox[List["-", FractionBox["1", SuperscriptBox[RowBox[List["(", RowBox[List["1", "+", "a"]], ")"]], "2"]]]]]], "/;", RowBox[List[RowBox[List["Re", "[", "a", "]"]], ">", RowBox[List["-", "1"]]]]]]]]

 MathML Form

 0 1 t a log ( t ) t - 1 ( a + 1 ) 2 /; Re ( a ) > - 1 Condition t 0 1 t a t -1 1 a 1 2 -1 a -1 [/itex]

 Rule Form

 Cell[BoxData[RowBox[List[RowBox[List["HoldPattern", "[", RowBox[List[SubsuperscriptBox["\[Integral]", "0", "1"], RowBox[List[RowBox[List[SuperscriptBox["t_", "a_"], " ", RowBox[List["Log", "[", "t_", "]"]]]], RowBox[List["\[DifferentialD]", "t_"]]]]]], "]"]], "\[RuleDelayed]", RowBox[List[RowBox[List["-", FractionBox["1", SuperscriptBox[RowBox[List["(", RowBox[List["1", "+", "a"]], ")"]], "2"]]]], "/;", RowBox[List[RowBox[List["Re", "[", "a", "]"]], ">", RowBox[List["-", "1"]]]]]]]]]]

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

 2001-10-29