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 Log

 http://functions.wolfram.com/01.04.21.0002.01

 Input Form

 Integrate[z^(\[Alpha] - 1) Log[z], z] == (z^\[Alpha]/\[Alpha]^2) (\[Alpha] Log[z] - 1)

 Standard Form

 Cell[BoxData[RowBox[List[RowBox[List["\[Integral]", RowBox[List[SuperscriptBox["z", RowBox[List["\[Alpha]", "-", "1"]]], RowBox[List["Log", "[", "z", "]"]], RowBox[List["\[DifferentialD]", "z"]]]]]], "\[Equal]", RowBox[List[FractionBox[RowBox[List[SuperscriptBox["z", "\[Alpha]"], " "]], SuperscriptBox["\[Alpha]", "2"]], RowBox[List["(", RowBox[List[RowBox[List["\[Alpha]", " ", RowBox[List["Log", "[", "z", "]"]]]], "-", "1"]], ")"]]]]]]]]

 MathML Form

 z α - 1 log ( z ) z z α ( α log ( z ) - 1 ) α 2 z z α -1 z z α α z -1 α 2 -1 [/itex]

 Rule Form

 Cell[BoxData[RowBox[List[RowBox[List["HoldPattern", "[", RowBox[List["\[Integral]", RowBox[List[RowBox[List[SuperscriptBox["z_", RowBox[List["\[Alpha]_", "-", "1"]]], " ", RowBox[List["Log", "[", "z_", "]"]]]], RowBox[List["\[DifferentialD]", "z_"]]]]]], "]"]], "\[RuleDelayed]", FractionBox[RowBox[List[SuperscriptBox["z", "\[Alpha]"], " ", RowBox[List["(", RowBox[List[RowBox[List["\[Alpha]", " ", RowBox[List["Log", "[", "z", "]"]]]], "-", "1"]], ")"]]]], SuperscriptBox["\[Alpha]", "2"]]]]]]

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

 2001-10-29