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 FractionalPart

 http://functions.wolfram.com/04.05.21.0003.01

 Input Form

 Integrate[(1/z) FractionalPart[z], z] == z (1 - Log[z]) + Log[z] FractionalPart[z]

 Standard Form

 Cell[BoxData[RowBox[List[RowBox[List["\[Integral]", RowBox[List[FractionBox["1", "z"], " ", RowBox[List["FractionalPart", "[", "z", "]"]], RowBox[List["\[DifferentialD]", "z"]]]]]], "\[Equal]", RowBox[List[RowBox[List["z", RowBox[List["(", RowBox[List["1", "-", RowBox[List["Log", "[", "z", "]"]]]], ")"]]]], "+", RowBox[List[RowBox[List["Log", "[", "z", "]"]], RowBox[List["FractionalPart", "[", "z", "]"]]]]]]]]]]

 MathML Form

 frac ( z ) z z z ( 1 - log ( z ) ) + frac ( z ) log ( z ) z FractionalPart z z -1 z 1 -1 z FractionalPart z z [/itex]

 Rule Form

 Cell[BoxData[RowBox[List[RowBox[List["HoldPattern", "[", RowBox[List["\[Integral]", RowBox[List[FractionBox[RowBox[List["FractionalPart", "[", "z_", "]"]], "z_"], RowBox[List["\[DifferentialD]", "z_"]]]]]], "]"]], "\[RuleDelayed]", RowBox[List[RowBox[List["z", " ", RowBox[List["(", RowBox[List["1", "-", RowBox[List["Log", "[", "z", "]"]]]], ")"]]]], "+", RowBox[List[RowBox[List["Log", "[", "z", "]"]], " ", RowBox[List["FractionalPart", "[", "z", "]"]]]]]]]]]]

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

 2001-10-29

© 1998-2013 Wolfram Research, Inc.