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variants of this functions
ArcTan




Mathematica Notation

Traditional Notation









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





http://functions.wolfram.com/01.15.21.0004.01









  


  








Input Form





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








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


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





2001-10-29