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Sech






Mathematica Notation

Traditional Notation









Elementary Functions > Sech[z] > Integration > Indefinite integration > Involving functions of the direct function and hyperbolic functions > Involving rational functions of the direct function and hyperbolic functions > Involving rational functions of coth > Involving (a coth(z)+b sech(z))-n





http://functions.wolfram.com/01.24.21.0457.01









  


  










Input Form





Integrate[1/(a Coth[z] + b Sech[z]), z] == (Csch[z] ((-b + Sqrt[-4 a^2 + b^2]) Log[-b + Sqrt[-4 a^2 + b^2] - 2 a Sinh[z]] + (b + Sqrt[-4 a^2 + b^2]) Log[b + Sqrt[-4 a^2 + b^2] + 2 a Sinh[z]]) Sech[z] (a + a Cosh[2 z] + 2 b Sinh[z]))/(4 a Sqrt[-4 a^2 + b^2] (a Coth[z] + b Sech[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["1", RowBox[List[RowBox[List["a_", " ", RowBox[List["Coth", "[", "z_", "]"]]]], "+", RowBox[List["b_", " ", RowBox[List["Sech", "[", "z_", "]"]]]]]]], RowBox[List["\[DifferentialD]", "z_"]]]]]], "]"]], "\[RuleDelayed]", FractionBox[RowBox[List[RowBox[List["Csch", "[", "z", "]"]], " ", RowBox[List["(", RowBox[List[RowBox[List[RowBox[List["(", RowBox[List[RowBox[List["-", "b"]], "+", SqrtBox[RowBox[List[RowBox[List[RowBox[List["-", "4"]], " ", SuperscriptBox["a", "2"]]], "+", SuperscriptBox["b", "2"]]]]]], ")"]], " ", RowBox[List["Log", "[", RowBox[List[RowBox[List["-", "b"]], "+", SqrtBox[RowBox[List[RowBox[List[RowBox[List["-", "4"]], " ", SuperscriptBox["a", "2"]]], "+", SuperscriptBox["b", "2"]]]], "-", RowBox[List["2", " ", "a", " ", RowBox[List["Sinh", "[", "z", "]"]]]]]], "]"]]]], "+", RowBox[List[RowBox[List["(", RowBox[List["b", "+", SqrtBox[RowBox[List[RowBox[List[RowBox[List["-", "4"]], " ", SuperscriptBox["a", "2"]]], "+", SuperscriptBox["b", "2"]]]]]], ")"]], " ", RowBox[List["Log", "[", RowBox[List["b", "+", SqrtBox[RowBox[List[RowBox[List[RowBox[List["-", "4"]], " ", SuperscriptBox["a", "2"]]], "+", SuperscriptBox["b", "2"]]]], "+", RowBox[List["2", " ", "a", " ", RowBox[List["Sinh", "[", "z", "]"]]]]]], "]"]]]]]], ")"]], " ", RowBox[List["Sech", "[", "z", "]"]], " ", RowBox[List["(", RowBox[List["a", "+", RowBox[List["a", " ", RowBox[List["Cosh", "[", RowBox[List["2", " ", "z"]], "]"]]]], "+", RowBox[List["2", " ", "b", " ", RowBox[List["Sinh", "[", "z", "]"]]]]]], ")"]]]], RowBox[List["4", " ", "a", " ", SqrtBox[RowBox[List[RowBox[List[RowBox[List["-", "4"]], " ", SuperscriptBox["a", "2"]]], "+", SuperscriptBox["b", "2"]]]], " ", RowBox[List["(", RowBox[List[RowBox[List["a", " ", RowBox[List["Coth", "[", "z", "]"]]]], "+", RowBox[List["b", " ", RowBox[List["Sech", "[", "z", "]"]]]]]], ")"]]]]]]]]]










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





2002-12-18





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