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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))n)beta





http://functions.wolfram.com/01.09.21.0182.01









  


  










Input Form





Integrate[Cot[c z]/Sqrt[(a + b Cot[c z])^3], z] == (-((2 a (a + b Cot[c z]))/(a^2 + b^2)) + (ArcTanh[Sqrt[a + b Cot[c z]]/Sqrt[a - I b]] (a + b Cot[c z])^(3/2))/ (a - I b)^(3/2) + (ArcTanh[Sqrt[a + b Cot[c z]]/Sqrt[a + I b]] (a + b Cot[c z])^(3/2))/(a + I b)^(3/2))/(c Sqrt[(a + b Cot[c z])^3])










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[RowBox[List["Cot", "[", RowBox[List["c_", " ", "z_"]], "]"]], SqrtBox[SuperscriptBox[RowBox[List["(", RowBox[List["a_", "+", RowBox[List["b_", " ", RowBox[List["Cot", "[", RowBox[List["c_", " ", "z_"]], "]"]]]]]], ")"]], "3"]]], RowBox[List["\[DifferentialD]", "z_"]]]]]], "]"]], "\[RuleDelayed]", FractionBox[RowBox[List[RowBox[List["-", FractionBox[RowBox[List["2", " ", "a", " ", RowBox[List["(", RowBox[List["a", "+", RowBox[List["b", " ", RowBox[List["Cot", "[", RowBox[List["c", " ", "z"]], "]"]]]]]], ")"]]]], RowBox[List[SuperscriptBox["a", "2"], "+", SuperscriptBox["b", "2"]]]]]], "+", FractionBox[RowBox[List[RowBox[List["ArcTanh", "[", FractionBox[SqrtBox[RowBox[List["a", "+", RowBox[List["b", " ", RowBox[List["Cot", "[", RowBox[List["c", " ", "z"]], "]"]]]]]]], SqrtBox[RowBox[List["a", "-", RowBox[List["\[ImaginaryI]", " ", "b"]]]]]], "]"]], " ", SuperscriptBox[RowBox[List["(", RowBox[List["a", "+", RowBox[List["b", " ", RowBox[List["Cot", "[", RowBox[List["c", " ", "z"]], "]"]]]]]], ")"]], RowBox[List["3", "/", "2"]]]]], SuperscriptBox[RowBox[List["(", RowBox[List["a", "-", RowBox[List["\[ImaginaryI]", " ", "b"]]]], ")"]], RowBox[List["3", "/", "2"]]]], "+", FractionBox[RowBox[List[RowBox[List["ArcTanh", "[", FractionBox[SqrtBox[RowBox[List["a", "+", RowBox[List["b", " ", RowBox[List["Cot", "[", RowBox[List["c", " ", "z"]], "]"]]]]]]], SqrtBox[RowBox[List["a", "+", RowBox[List["\[ImaginaryI]", " ", "b"]]]]]], "]"]], " ", SuperscriptBox[RowBox[List["(", RowBox[List["a", "+", RowBox[List["b", " ", RowBox[List["Cot", "[", RowBox[List["c", " ", "z"]], "]"]]]]]], ")"]], RowBox[List["3", "/", "2"]]]]], SuperscriptBox[RowBox[List["(", RowBox[List["a", "+", RowBox[List["\[ImaginaryI]", " ", "b"]]]], ")"]], RowBox[List["3", "/", "2"]]]]]], RowBox[List["c", " ", SqrtBox[SuperscriptBox[RowBox[List["(", RowBox[List["a", "+", RowBox[List["b", " ", RowBox[List["Cot", "[", RowBox[List["c", " ", "z"]], "]"]]]]]], ")"]], "3"]]]]]]]]]










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





2002-12-18