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Csch






Mathematica Notation

Traditional Notation









Elementary Functions > Csch[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 csch2(c z))beta





http://functions.wolfram.com/01.23.21.0454.01









  


  










Input Form





Integrate[Tanh[c z]/Sqrt[a + b Csch[c z]^2], z] == (I ((I ArcTan[(Sqrt[-2 a + 2 b] Sinh[c z])/Sqrt[-a + 2 b + a Cosh[2 c z]]])/ Sqrt[-2 a + 2 b] - (I ArcTanh[(Sqrt[2] Sqrt[a] Sinh[c z])/ Sqrt[-a + 2 b + a Cosh[2 c z]]])/(Sqrt[2] Sqrt[a])) Sqrt[-a + 2 b + a Cosh[2 c z]] Csch[c z])/(c Sqrt[a + b Csch[c z]^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[FractionBox[RowBox[List["Tanh", "[", RowBox[List["c_", " ", "z_"]], "]"]], SqrtBox[RowBox[List["a_", "+", RowBox[List["b_", " ", SuperscriptBox[RowBox[List["Csch", "[", RowBox[List["c_", " ", "z_"]], "]"]], "2"]]]]]]], RowBox[List["\[DifferentialD]", "z_"]]]]]], "]"]], "\[RuleDelayed]", FractionBox[RowBox[List["\[ImaginaryI]", " ", RowBox[List["(", RowBox[List[FractionBox[RowBox[List["\[ImaginaryI]", " ", RowBox[List["ArcTan", "[", FractionBox[RowBox[List[SqrtBox[RowBox[List[RowBox[List[RowBox[List["-", "2"]], " ", "a"]], "+", RowBox[List["2", " ", "b"]]]]], " ", RowBox[List["Sinh", "[", RowBox[List["c", " ", "z"]], "]"]]]], SqrtBox[RowBox[List[RowBox[List["-", "a"]], "+", RowBox[List["2", " ", "b"]], "+", RowBox[List["a", " ", RowBox[List["Cosh", "[", RowBox[List["2", " ", "c", " ", "z"]], "]"]]]]]]]], "]"]]]], SqrtBox[RowBox[List[RowBox[List[RowBox[List["-", "2"]], " ", "a"]], "+", RowBox[List["2", " ", "b"]]]]]], "-", FractionBox[RowBox[List["\[ImaginaryI]", " ", RowBox[List["ArcTanh", "[", FractionBox[RowBox[List[SqrtBox["2"], " ", SqrtBox["a"], " ", RowBox[List["Sinh", "[", RowBox[List["c", " ", "z"]], "]"]]]], SqrtBox[RowBox[List[RowBox[List["-", "a"]], "+", RowBox[List["2", " ", "b"]], "+", RowBox[List["a", " ", RowBox[List["Cosh", "[", RowBox[List["2", " ", "c", " ", "z"]], "]"]]]]]]]], "]"]]]], RowBox[List[SqrtBox["2"], " ", SqrtBox["a"]]]]]], ")"]], " ", SqrtBox[RowBox[List[RowBox[List["-", "a"]], "+", RowBox[List["2", " ", "b"]], "+", RowBox[List["a", " ", RowBox[List["Cosh", "[", RowBox[List["2", " ", "c", " ", "z"]], "]"]]]]]]], " ", RowBox[List["Csch", "[", RowBox[List["c", " ", "z"]], "]"]]]], RowBox[List["c", " ", SqrtBox[RowBox[List["a", "+", RowBox[List["b", " ", SuperscriptBox[RowBox[List["Csch", "[", RowBox[List["c", " ", "z"]], "]"]], "2"]]]]]]]]]]]]]










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





2002-12-18