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Coth






Mathematica Notation

Traditional Notation









Elementary Functions > Coth[z] > Integration > Indefinite integration > Involving functions of the direct function and hyperbolic functions > Involving algebraic functions of the direct function and hyperbolic functions > Involving tanh > Involving tanh(c z)(a+b coth2(c z))beta





http://functions.wolfram.com/01.22.21.0411.01









  


  










Input Form





Integrate[Tanh[c z] Sqrt[a + b Coth[c z]^2], z] == ((-Sqrt[a]) Sqrt[a + b] ArcSinh[(Sqrt[a] Tanh[c z])/Sqrt[b]] (b Coth[c z] + a Tanh[c z]) + Sqrt[b] (a + b) ArcTanh[Sqrt[a + b Coth[c z]^2]/Sqrt[a + b]] Sqrt[a + b Coth[c z]^2] Sqrt[1 + (a Tanh[c z]^2)/b])/(Sqrt[b] Sqrt[a + b] c Sqrt[a + b Coth[c z]^2] Sqrt[1 + (a Tanh[c z]^2)/b])










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["Tanh", "[", RowBox[List["c_", " ", "z_"]], "]"]], " ", SqrtBox[RowBox[List["a_", "+", RowBox[List["b_", " ", SuperscriptBox[RowBox[List["Coth", "[", RowBox[List["c_", " ", "z_"]], "]"]], "2"]]]]]]]], RowBox[List["\[DifferentialD]", "z_"]]]]]], "]"]], "\[RuleDelayed]", FractionBox[RowBox[List[RowBox[List[RowBox[List["-", SqrtBox["a"]]], " ", SqrtBox[RowBox[List["a", "+", "b"]]], " ", RowBox[List["ArcSinh", "[", FractionBox[RowBox[List[SqrtBox["a"], " ", RowBox[List["Tanh", "[", RowBox[List["c", " ", "z"]], "]"]]]], SqrtBox["b"]], "]"]], " ", RowBox[List["(", RowBox[List[RowBox[List["b", " ", RowBox[List["Coth", "[", RowBox[List["c", " ", "z"]], "]"]]]], "+", RowBox[List["a", " ", RowBox[List["Tanh", "[", RowBox[List["c", " ", "z"]], "]"]]]]]], ")"]]]], "+", RowBox[List[SqrtBox["b"], " ", RowBox[List["(", RowBox[List["a", "+", "b"]], ")"]], " ", RowBox[List["ArcTanh", "[", FractionBox[SqrtBox[RowBox[List["a", "+", RowBox[List["b", " ", SuperscriptBox[RowBox[List["Coth", "[", RowBox[List["c", " ", "z"]], "]"]], "2"]]]]]], SqrtBox[RowBox[List["a", "+", "b"]]]], "]"]], " ", SqrtBox[RowBox[List["a", "+", RowBox[List["b", " ", SuperscriptBox[RowBox[List["Coth", "[", RowBox[List["c", " ", "z"]], "]"]], "2"]]]]]], " ", SqrtBox[RowBox[List["1", "+", FractionBox[RowBox[List["a", " ", SuperscriptBox[RowBox[List["Tanh", "[", RowBox[List["c", " ", "z"]], "]"]], "2"]]], "b"]]]]]]]], RowBox[List[SqrtBox["b"], " ", SqrtBox[RowBox[List["a", "+", "b"]]], " ", "c", " ", SqrtBox[RowBox[List["a", "+", RowBox[List["b", " ", SuperscriptBox[RowBox[List["Coth", "[", RowBox[List["c", " ", "z"]], "]"]], "2"]]]]]], " ", SqrtBox[RowBox[List["1", "+", FractionBox[RowBox[List["a", " ", SuperscriptBox[RowBox[List["Tanh", "[", RowBox[List["c", " ", "z"]], "]"]], "2"]]], "b"]]]]]]]]]]]










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





2002-12-18





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