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Coth




Mathematica Notation

Traditional Notation









Elementary Functions > Coth[z] > Integration > Indefinite integration > Involving one direct function and elementary functions > Involving hyperbolic functions > Involving algebraic functions of cosh > Involving cosh(c z)(a+b cosh(2c z))beta





http://functions.wolfram.com/01.22.21.0139.01









  


  








Input Form





Integrate[(Cosh[c z] Coth[c z])/Sqrt[a + b Cosh[2 c z]], z] == (1/(2 c)) (-((2 ArcTanh[(Sqrt[a + b] Cosh[c z])/Sqrt[a + b Cosh[2 c z]]])/ Sqrt[a + b]) + (Sqrt[2] Log[Sqrt[2] Sqrt[b] Cosh[c z] + Sqrt[a + b Cosh[2 c z]]])/Sqrt[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[FractionBox[RowBox[List[RowBox[List["Cosh", "[", RowBox[List["c_", " ", "z_"]], "]"]], " ", RowBox[List["Coth", "[", RowBox[List["c_", " ", "z_"]], "]"]]]], SqrtBox[RowBox[List["a_", "+", RowBox[List["b_", " ", RowBox[List["Cosh", "[", RowBox[List["2", " ", "c_", " ", "z_"]], "]"]]]]]]]], RowBox[List["\[DifferentialD]", "z_"]]]]]], "]"]], "\[RuleDelayed]", FractionBox[RowBox[List[RowBox[List["-", FractionBox[RowBox[List["2", " ", RowBox[List["ArcTanh", "[", FractionBox[RowBox[List[SqrtBox[RowBox[List["a", "+", "b"]]], " ", RowBox[List["Cosh", "[", RowBox[List["c", " ", "z"]], "]"]]]], SqrtBox[RowBox[List["a", "+", RowBox[List["b", " ", RowBox[List["Cosh", "[", RowBox[List["2", " ", "c", " ", "z"]], "]"]]]]]]]], "]"]]]], SqrtBox[RowBox[List["a", "+", "b"]]]]]], "+", FractionBox[RowBox[List[SqrtBox["2"], " ", RowBox[List["Log", "[", RowBox[List[RowBox[List[SqrtBox["2"], " ", SqrtBox["b"], " ", RowBox[List["Cosh", "[", RowBox[List["c", " ", "z"]], "]"]]]], "+", SqrtBox[RowBox[List["a", "+", RowBox[List["b", " ", RowBox[List["Cosh", "[", RowBox[List["2", " ", "c", " ", "z"]], "]"]]]]]]]]], "]"]]]], SqrtBox["b"]]]], RowBox[List["2", " ", "c"]]]]]]]


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





2002-12-18