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Csch






Mathematica Notation

Traditional Notation









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





http://functions.wolfram.com/01.23.21.0099.01









  


  










Input Form





Integrate[Csch[c z]/Sqrt[a - I a Sinh[c z]], z] == ((2 I ArcTan[Coth[(c z)/4]] - 2 I ArcTan[Tanh[(c z)/4]] + 4 Sqrt[2] ArcTanh[(1 + I Tanh[(c z)/4])/Sqrt[2]] - Log[Cosh[(c z)/4]^2 Cosh[(c z)/2]] + Log[Cosh[(c z)/2] Sinh[(c z)/4]^2]) (Cosh[(c z)/2] - I Sinh[(c z)/2]))/(2 c Sqrt[a - I a Sinh[c z]])










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["Csch", "[", RowBox[List["c_", " ", "z_"]], "]"]], SqrtBox[RowBox[List["a_", "-", RowBox[List["\[ImaginaryI]", " ", "a_", " ", RowBox[List["Sinh", "[", RowBox[List["c_", " ", "z_"]], "]"]]]]]]]], RowBox[List["\[DifferentialD]", "z_"]]]]]], "]"]], "\[RuleDelayed]", FractionBox[RowBox[List[RowBox[List["(", RowBox[List[RowBox[List["2", " ", "\[ImaginaryI]", " ", RowBox[List["ArcTan", "[", RowBox[List["Coth", "[", FractionBox[RowBox[List["c", " ", "z"]], "4"], "]"]], "]"]]]], "-", RowBox[List["2", " ", "\[ImaginaryI]", " ", RowBox[List["ArcTan", "[", RowBox[List["Tanh", "[", FractionBox[RowBox[List["c", " ", "z"]], "4"], "]"]], "]"]]]], "+", RowBox[List["4", " ", SqrtBox["2"], " ", RowBox[List["ArcTanh", "[", FractionBox[RowBox[List["1", "+", RowBox[List["\[ImaginaryI]", " ", RowBox[List["Tanh", "[", FractionBox[RowBox[List["c", " ", "z"]], "4"], "]"]]]]]], SqrtBox["2"]], "]"]]]], "-", RowBox[List["Log", "[", RowBox[List[SuperscriptBox[RowBox[List["Cosh", "[", FractionBox[RowBox[List["c", " ", "z"]], "4"], "]"]], "2"], " ", RowBox[List["Cosh", "[", FractionBox[RowBox[List["c", " ", "z"]], "2"], "]"]]]], "]"]], "+", RowBox[List["Log", "[", RowBox[List[RowBox[List["Cosh", "[", FractionBox[RowBox[List["c", " ", "z"]], "2"], "]"]], " ", SuperscriptBox[RowBox[List["Sinh", "[", FractionBox[RowBox[List["c", " ", "z"]], "4"], "]"]], "2"]]], "]"]]]], ")"]], " ", RowBox[List["(", RowBox[List[RowBox[List["Cosh", "[", FractionBox[RowBox[List["c", " ", "z"]], "2"], "]"]], "-", RowBox[List["\[ImaginaryI]", " ", RowBox[List["Sinh", "[", FractionBox[RowBox[List["c", " ", "z"]], "2"], "]"]]]]]], ")"]]]], RowBox[List["2", " ", "c", " ", SqrtBox[RowBox[List["a", "-", RowBox[List["\[ImaginaryI]", " ", "a", " ", RowBox[List["Sinh", "[", RowBox[List["c", " ", "z"]], "]"]]]]]]]]]]]]]]










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





2002-12-18





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