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Coth






Mathematica Notation

Traditional Notation









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





http://functions.wolfram.com/01.22.21.0266.01









  


  










Input Form





Integrate[Coth[c z] Sqrt[(a + b Coth[c z])^3], z] == Sqrt[(a + b Coth[c z])^3] ((3 (a - b)^(3/2) ArcTanh[Sqrt[a + b Coth[c z]]/Sqrt[a - b]] + 3 (a + b)^(3/2) ArcTanh[Sqrt[a + b Coth[c z]]/Sqrt[a + b]] - 2 Sqrt[a + b Coth[c z]] (4 a + b Coth[c z]))/ (3 c (a + b Coth[c z])^(3/2)))










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[RowBox[List["Coth", "[", RowBox[List["c_", " ", "z_"]], "]"]], " ", SqrtBox[SuperscriptBox[RowBox[List["(", RowBox[List["a_", "+", RowBox[List["b_", " ", RowBox[List["Coth", "[", RowBox[List["c_", " ", "z_"]], "]"]]]]]], ")"]], "3"]]]], RowBox[List["\[DifferentialD]", "z_"]]]]]], "]"]], "\[RuleDelayed]", FractionBox[RowBox[List[SqrtBox[SuperscriptBox[RowBox[List["(", RowBox[List["a", "+", RowBox[List["b", " ", RowBox[List["Coth", "[", RowBox[List["c", " ", "z"]], "]"]]]]]], ")"]], "3"]], " ", RowBox[List["(", RowBox[List[RowBox[List["3", " ", SuperscriptBox[RowBox[List["(", RowBox[List["a", "-", "b"]], ")"]], RowBox[List["3", "/", "2"]]], " ", RowBox[List["ArcTanh", "[", FractionBox[SqrtBox[RowBox[List["a", "+", RowBox[List["b", " ", RowBox[List["Coth", "[", RowBox[List["c", " ", "z"]], "]"]]]]]]], SqrtBox[RowBox[List["a", "-", "b"]]]], "]"]]]], "+", RowBox[List["3", " ", SuperscriptBox[RowBox[List["(", RowBox[List["a", "+", "b"]], ")"]], RowBox[List["3", "/", "2"]]], " ", RowBox[List["ArcTanh", "[", FractionBox[SqrtBox[RowBox[List["a", "+", RowBox[List["b", " ", RowBox[List["Coth", "[", RowBox[List["c", " ", "z"]], "]"]]]]]]], SqrtBox[RowBox[List["a", "+", "b"]]]], "]"]]]], "-", RowBox[List["2", " ", SqrtBox[RowBox[List["a", "+", RowBox[List["b", " ", RowBox[List["Coth", "[", RowBox[List["c", " ", "z"]], "]"]]]]]]], " ", RowBox[List["(", RowBox[List[RowBox[List["4", " ", "a"]], "+", RowBox[List["b", " ", RowBox[List["Coth", "[", RowBox[List["c", " ", "z"]], "]"]]]]]], ")"]]]]]], ")"]]]], RowBox[List["3", " ", "c", " ", SuperscriptBox[RowBox[List["(", RowBox[List["a", "+", RowBox[List["b", " ", RowBox[List["Coth", "[", RowBox[List["c", " ", "z"]], "]"]]]]]], ")"]], RowBox[List["3", "/", "2"]]]]]]]]]]










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





2002-12-18





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