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 | | http://functions.wolfram.com/01.09.21.0189.01 | 
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 | | Integrate[((a + b Cot[c z]^2)^n)^\[Beta], z] == 
 (-(1/c)) ((AppellF1[1/2, 1, (-n) \[Beta], 3/2, -Cot[c z]^2, 
     -((b Cot[c z]^2)/a)] Cot[c z] ((a + b Cot[c z]^2)^n)^\[Beta])/
   (1 + (b Cot[c z]^2)/a)^(n \[Beta])) | 
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 | | Cell[BoxData[RowBox[List[RowBox[List["\[Integral]", RowBox[List[SuperscriptBox[RowBox[List["(", SuperscriptBox[RowBox[List["(", RowBox[List["a", "+", RowBox[List["b", " ", SuperscriptBox[RowBox[List["Cot", "[", RowBox[List["c", " ", "z"]], "]"]], "2"]]]]], ")"]], "n"], ")"]], "\[Beta]"], RowBox[List["\[DifferentialD]", "z"]]]]]], "\[Equal]", RowBox[List[RowBox[List["-", FractionBox["1", "c"]]], RowBox[List["(", RowBox[List[RowBox[List["AppellF1", "[", RowBox[List[FractionBox["1", "2"], ",", "1", ",", RowBox[List[RowBox[List["-", "n"]], " ", "\[Beta]"]], ",", FractionBox["3", "2"], ",", RowBox[List["-", SuperscriptBox[RowBox[List["Cot", "[", RowBox[List["c", " ", "z"]], "]"]], "2"]]], ",", RowBox[List["-", FractionBox[RowBox[List["b", " ", SuperscriptBox[RowBox[List["Cot", "[", RowBox[List["c", " ", "z"]], "]"]], "2"]]], "a"]]]]], "]"]], " ", RowBox[List["Cot", "[", RowBox[List["c", " ", "z"]], "]"]], " ", SuperscriptBox[RowBox[List["(", SuperscriptBox[RowBox[List["(", RowBox[List["a", "+", RowBox[List["b", " ", SuperscriptBox[RowBox[List["Cot", "[", RowBox[List["c", " ", "z"]], "]"]], "2"]]]]], ")"]], "n"], ")"]], "\[Beta]"], " ", SuperscriptBox[RowBox[List["(", RowBox[List["1", "+", FractionBox[RowBox[List["b", " ", SuperscriptBox[RowBox[List["Cot", "[", RowBox[List["c", " ", "z"]], "]"]], "2"]]], "a"]]], ")"]], RowBox[List[RowBox[List["-", "n"]], " ", "\[Beta]"]]]]], ")"]]]]]]]] | 
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 | | Cell[BoxData[RowBox[List[RowBox[List["HoldPattern", "[", RowBox[List["\[Integral]", RowBox[List[SuperscriptBox[RowBox[List["(", SuperscriptBox[RowBox[List["(", RowBox[List["a_", "+", RowBox[List["b_", " ", SuperscriptBox[RowBox[List["Cot", "[", RowBox[List["c_", " ", "z_"]], "]"]], "2"]]]]], ")"]], "n_"], ")"]], "\[Beta]_"], RowBox[List["\[DifferentialD]", "z_"]]]]]], "]"]], "\[RuleDelayed]", RowBox[List["-", FractionBox[RowBox[List[RowBox[List["AppellF1", "[", RowBox[List[FractionBox["1", "2"], ",", "1", ",", RowBox[List[RowBox[List["-", "n"]], " ", "\[Beta]"]], ",", FractionBox["3", "2"], ",", RowBox[List["-", SuperscriptBox[RowBox[List["Cot", "[", RowBox[List["c", " ", "z"]], "]"]], "2"]]], ",", RowBox[List["-", FractionBox[RowBox[List["b", " ", SuperscriptBox[RowBox[List["Cot", "[", RowBox[List["c", " ", "z"]], "]"]], "2"]]], "a"]]]]], "]"]], " ", RowBox[List["Cot", "[", RowBox[List["c", " ", "z"]], "]"]], " ", SuperscriptBox[RowBox[List["(", SuperscriptBox[RowBox[List["(", RowBox[List["a", "+", RowBox[List["b", " ", SuperscriptBox[RowBox[List["Cot", "[", RowBox[List["c", " ", "z"]], "]"]], "2"]]]]], ")"]], "n"], ")"]], "\[Beta]"], " ", SuperscriptBox[RowBox[List["(", RowBox[List["1", "+", FractionBox[RowBox[List["b", " ", SuperscriptBox[RowBox[List["Cot", "[", RowBox[List["c", " ", "z"]], "]"]], "2"]]], "a"]]], ")"]], RowBox[List[RowBox[List["-", "n"]], " ", "\[Beta]"]]]]], "c"]]]]]]] | 
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 | | Date Added to functions.wolfram.com (modification date) | 
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