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variants of this functions
ArcTan






Mathematica Notation

Traditional Notation









Elementary Functions > ArcTan[x,y] > Integration > Indefinite integration > With respect to x





http://functions.wolfram.com/01.15.21.0002.01









  


  










Input Form





Integrate[x^(\[Alpha] - 1) ArcTan[x, y], x] == (x^\[Alpha] ArcTan[x, y])/\[Alpha] + (x^(1 + \[Alpha])/(y \[Alpha] (1 + \[Alpha]))) Hypergeometric2F1[(1 + \[Alpha])/2, 1, (3 + \[Alpha])/2, -(x^2/y^2)]










Standard Form





Cell[BoxData[RowBox[List[RowBox[List["\[Integral]", RowBox[List[SuperscriptBox["x", RowBox[List["\[Alpha]", "-", "1"]]], RowBox[List["ArcTan", "[", RowBox[List["x", ",", "y"]], "]"]], RowBox[List["\[DifferentialD]", "x"]]]]]], "\[Equal]", RowBox[List[FractionBox[RowBox[List[SuperscriptBox["x", "\[Alpha]"], " ", RowBox[List["ArcTan", "[", RowBox[List["x", ",", "y"]], "]"]]]], "\[Alpha]"], "+", RowBox[List[FractionBox[RowBox[List[SuperscriptBox["x", RowBox[List["1", "+", "\[Alpha]"]]], " "]], RowBox[List["y", " ", "\[Alpha]", " ", RowBox[List["(", RowBox[List["1", "+", "\[Alpha]"]], ")"]]]]], RowBox[List["Hypergeometric2F1", "[", RowBox[List[FractionBox[RowBox[List["1", "+", "\[Alpha]"]], "2"], ",", "1", ",", FractionBox[RowBox[List["3", "+", "\[Alpha]"]], "2"], ",", RowBox[List["-", FractionBox[SuperscriptBox["x", "2"], SuperscriptBox["y", "2"]]]]]], "]"]]]]]]]]]]










MathML Form







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Rule Form





Cell[BoxData[RowBox[List[RowBox[List["HoldPattern", "[", RowBox[List["\[Integral]", RowBox[List[RowBox[List[SuperscriptBox["x_", RowBox[List["\[Alpha]_", "-", "1"]]], " ", RowBox[List["ArcTan", "[", RowBox[List["x_", ",", "y_"]], "]"]]]], RowBox[List["\[DifferentialD]", "x_"]]]]]], "]"]], "\[RuleDelayed]", RowBox[List[FractionBox[RowBox[List[SuperscriptBox["x", "\[Alpha]"], " ", RowBox[List["ArcTan", "[", RowBox[List["x", ",", "y"]], "]"]]]], "\[Alpha]"], "+", FractionBox[RowBox[List[SuperscriptBox["x", RowBox[List["1", "+", "\[Alpha]"]]], " ", RowBox[List["Hypergeometric2F1", "[", RowBox[List[FractionBox[RowBox[List["1", "+", "\[Alpha]"]], "2"], ",", "1", ",", FractionBox[RowBox[List["3", "+", "\[Alpha]"]], "2"], ",", RowBox[List["-", FractionBox[SuperscriptBox["x", "2"], SuperscriptBox["y", "2"]]]]]], "]"]]]], RowBox[List["y", " ", "\[Alpha]", " ", RowBox[List["(", RowBox[List["1", "+", "\[Alpha]"]], ")"]]]]]]]]]]]










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





2001-10-29





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