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variants of this functions
Log






Mathematica Notation

Traditional Notation









Elementary Functions > Log[z] > Integration > Indefinite integration > Involving the direct function





http://functions.wolfram.com/01.04.21.0009.01









  


  










Input Form





Integrate[Log[a + b z]^2/(e + f z), z] == (1/f) (Log[a + b z]^2 Log[(b (e + f z))/(b e - a f)] + 2 Log[a + b z] PolyLog[2, (f (a + b z))/((-b) e + a f)] - 2 PolyLog[3, (f (a + b z))/((-b) e + a f)])










Standard Form





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MathML Form







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Rule Form





Cell[BoxData[RowBox[List[RowBox[List["HoldPattern", "[", RowBox[List["\[Integral]", RowBox[List[FractionBox[SuperscriptBox[RowBox[List["Log", "[", RowBox[List["a_", "+", RowBox[List["b_", " ", "z_"]]]], "]"]], "2"], RowBox[List["e_", "+", RowBox[List["f_", " ", "z_"]]]]], RowBox[List["\[DifferentialD]", "z_"]]]]]], "]"]], "\[RuleDelayed]", FractionBox[RowBox[List[RowBox[List[SuperscriptBox[RowBox[List["Log", "[", RowBox[List["a", "+", RowBox[List["b", " ", "z"]]]], "]"]], "2"], " ", RowBox[List["Log", "[", FractionBox[RowBox[List["b", " ", RowBox[List["(", RowBox[List["e", "+", RowBox[List["f", " ", "z"]]]], ")"]]]], RowBox[List[RowBox[List["b", " ", "e"]], "-", RowBox[List["a", " ", "f"]]]]], "]"]]]], "+", RowBox[List["2", " ", RowBox[List["Log", "[", RowBox[List["a", "+", RowBox[List["b", " ", "z"]]]], "]"]], " ", RowBox[List["PolyLog", "[", RowBox[List["2", ",", FractionBox[RowBox[List["f", " ", RowBox[List["(", RowBox[List["a", "+", RowBox[List["b", " ", "z"]]]], ")"]]]], RowBox[List[RowBox[List[RowBox[List["-", "b"]], " ", "e"]], "+", RowBox[List["a", " ", "f"]]]]]]], "]"]]]], "-", RowBox[List["2", " ", RowBox[List["PolyLog", "[", RowBox[List["3", ",", FractionBox[RowBox[List["f", " ", RowBox[List["(", RowBox[List["a", "+", RowBox[List["b", " ", "z"]]]], ")"]]]], RowBox[List[RowBox[List[RowBox[List["-", "b"]], " ", "e"]], "+", RowBox[List["a", " ", "f"]]]]]]], "]"]]]]]], "f"]]]]]










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





2001-10-29





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