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Cot






Mathematica Notation

Traditional Notation









Elementary Functions > Cot[z] > Integration > Indefinite integration > Involving functions of the direct function > Involving algebraic functions of the direct function > Involving (a+b cot(c z))beta





http://functions.wolfram.com/01.09.21.0174.01









  


  










Input Form





Integrate[Cot[c z] (a + b Cot[c z])^\[Beta], z] == ((a + b Cot[c z])^(1 + \[Beta]) ((a + I b) Hypergeometric2F1[1 + \[Beta], 1, 2 + \[Beta], (a + b Cot[c z])/(a - I b)] + (a - I b) Hypergeometric2F1[1 + \[Beta], 1, 2 + \[Beta], (a + b Cot[c z])/(a + I b)]))/ (2 (a^2 + b^2) c (1 + \[Beta]))










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[RowBox[List["Cot", "[", RowBox[List["c_", " ", "z_"]], "]"]], " ", SuperscriptBox[RowBox[List["(", RowBox[List["a_", "+", RowBox[List["b_", " ", RowBox[List["Cot", "[", RowBox[List["c_", " ", "z_"]], "]"]]]]]], ")"]], "\[Beta]_"]]], RowBox[List["\[DifferentialD]", "z_"]]]]]], "]"]], "\[RuleDelayed]", FractionBox[RowBox[List[SuperscriptBox[RowBox[List["(", RowBox[List["a", "+", RowBox[List["b", " ", RowBox[List["Cot", "[", RowBox[List["c", " ", "z"]], "]"]]]]]], ")"]], RowBox[List["1", "+", "\[Beta]"]]], " ", RowBox[List["(", RowBox[List[RowBox[List[RowBox[List["(", RowBox[List["a", "+", RowBox[List["\[ImaginaryI]", " ", "b"]]]], ")"]], " ", RowBox[List["Hypergeometric2F1", "[", RowBox[List[RowBox[List["1", "+", "\[Beta]"]], ",", "1", ",", RowBox[List["2", "+", "\[Beta]"]], ",", FractionBox[RowBox[List["a", "+", RowBox[List["b", " ", RowBox[List["Cot", "[", RowBox[List["c", " ", "z"]], "]"]]]]]], RowBox[List["a", "-", RowBox[List["\[ImaginaryI]", " ", "b"]]]]]]], "]"]]]], "+", RowBox[List[RowBox[List["(", RowBox[List["a", "-", RowBox[List["\[ImaginaryI]", " ", "b"]]]], ")"]], " ", RowBox[List["Hypergeometric2F1", "[", RowBox[List[RowBox[List["1", "+", "\[Beta]"]], ",", "1", ",", RowBox[List["2", "+", "\[Beta]"]], ",", FractionBox[RowBox[List["a", "+", RowBox[List["b", " ", RowBox[List["Cot", "[", RowBox[List["c", " ", "z"]], "]"]]]]]], RowBox[List["a", "+", RowBox[List["\[ImaginaryI]", " ", "b"]]]]]]], "]"]]]]]], ")"]]]], RowBox[List["2", " ", RowBox[List["(", RowBox[List[SuperscriptBox["a", "2"], "+", SuperscriptBox["b", "2"]]], ")"]], " ", "c", " ", RowBox[List["(", RowBox[List["1", "+", "\[Beta]"]], ")"]]]]]]]]]










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





2002-12-18