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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 rational functions of sinh > Involving 1/a+b sinh(d z)





http://functions.wolfram.com/01.23.21.0093.01









  


  










Input Form





Integrate[((A + B Sinh[z]) Csch[z])/(a + b Sinh[z]), z] == (1/(a Sqrt[-a^2 - b^2])) ((-2 A b + 2 a B) ArcTan[(b - a Tanh[z/2])/Sqrt[-a^2 - b^2]] + A Sqrt[-a^2 - b^2] (-Log[Cosh[z/2]] + Log[Sinh[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[RowBox[List["(", RowBox[List["A_", "+", RowBox[List["B_", " ", RowBox[List["Sinh", "[", "z_", "]"]]]]]], ")"]], " ", RowBox[List["Csch", "[", "z_", "]"]]]], RowBox[List["a_", "+", RowBox[List["b_", " ", RowBox[List["Sinh", "[", "z_", "]"]]]]]]], RowBox[List["\[DifferentialD]", "z_"]]]]]], "]"]], "\[RuleDelayed]", FractionBox[RowBox[List[RowBox[List[RowBox[List["(", RowBox[List[RowBox[List[RowBox[List["-", "2"]], " ", "A", " ", "b"]], "+", RowBox[List["2", " ", "a", " ", "B"]]]], ")"]], " ", RowBox[List["ArcTan", "[", FractionBox[RowBox[List["b", "-", RowBox[List["a", " ", RowBox[List["Tanh", "[", FractionBox["z", "2"], "]"]]]]]], SqrtBox[RowBox[List[RowBox[List["-", SuperscriptBox["a", "2"]]], "-", SuperscriptBox["b", "2"]]]]], "]"]]]], "+", RowBox[List["A", " ", SqrtBox[RowBox[List[RowBox[List["-", SuperscriptBox["a", "2"]]], "-", SuperscriptBox["b", "2"]]]], " ", RowBox[List["(", RowBox[List[RowBox[List["-", RowBox[List["Log", "[", RowBox[List["Cosh", "[", FractionBox["z", "2"], "]"]], "]"]]]], "+", RowBox[List["Log", "[", RowBox[List["Sinh", "[", FractionBox["z", "2"], "]"]], "]"]]]], ")"]]]]]], RowBox[List["a", " ", SqrtBox[RowBox[List[RowBox[List["-", SuperscriptBox["a", "2"]]], "-", SuperscriptBox["b", "2"]]]]]]]]]]]










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





2002-12-18





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