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Cosh




Mathematica Notation

Traditional Notation









Elementary Functions > Cosh[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 sinh > Involving (a+b sinh(e z)+c cosh(e z))-n





http://functions.wolfram.com/01.20.21.4277.01









  


  








Input Form





Integrate[(A + B Sinh[e z] + C Cosh[e z])/(a + b Sinh[e z] + c Cosh[e z]), z] == (1/((-b + c) (b + c))) (((-b) B + c C) z + (2 ((-A) b^2 + a b B + A c^2 - a c C) ArcTan[(b + (-a + c) Tanh[(e z)/2])/ Sqrt[-a^2 - b^2 + c^2]])/(Sqrt[-a^2 - b^2 + c^2] e) + ((B c - b C) Log[a + c Cosh[e z] + b Sinh[e z]])/e)








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["A_", "+", RowBox[List["B_", " ", RowBox[List["Sinh", "[", RowBox[List["e_", " ", "z_"]], "]"]]]], "+", RowBox[List["C", " ", RowBox[List["Cosh", "[", RowBox[List["e_", " ", "z_"]], "]"]]]]]], RowBox[List["a_", "+", RowBox[List["b_", " ", RowBox[List["Sinh", "[", RowBox[List["e_", " ", "z_"]], "]"]]]], "+", RowBox[List["c_", " ", RowBox[List["Cosh", "[", RowBox[List["e_", " ", "z_"]], "]"]]]]]]], RowBox[List["\[DifferentialD]", "z_"]]]]]], "]"]], "\[RuleDelayed]", FractionBox[RowBox[List[RowBox[List[RowBox[List["(", RowBox[List[RowBox[List[RowBox[List["-", "b"]], " ", "B"]], "+", RowBox[List["c", " ", "C"]]]], ")"]], " ", "z"]], "+", FractionBox[RowBox[List["2", " ", RowBox[List["(", RowBox[List[RowBox[List[RowBox[List["-", "A"]], " ", SuperscriptBox["b", "2"]]], "+", RowBox[List["a", " ", "b", " ", "B"]], "+", RowBox[List["A", " ", SuperscriptBox["c", "2"]]], "-", RowBox[List["a", " ", "c", " ", "C"]]]], ")"]], " ", RowBox[List["ArcTan", "[", FractionBox[RowBox[List["b", "+", RowBox[List[RowBox[List["(", RowBox[List[RowBox[List["-", "a"]], "+", "c"]], ")"]], " ", RowBox[List["Tanh", "[", FractionBox[RowBox[List["e", " ", "z"]], "2"], "]"]]]]]], SqrtBox[RowBox[List[RowBox[List["-", SuperscriptBox["a", "2"]]], "-", SuperscriptBox["b", "2"], "+", SuperscriptBox["c", "2"]]]]], "]"]]]], RowBox[List[SqrtBox[RowBox[List[RowBox[List["-", SuperscriptBox["a", "2"]]], "-", SuperscriptBox["b", "2"], "+", SuperscriptBox["c", "2"]]]], " ", "e"]]], "+", FractionBox[RowBox[List[RowBox[List["(", RowBox[List[RowBox[List["B", " ", "c"]], "-", RowBox[List["b", " ", "C"]]]], ")"]], " ", RowBox[List["Log", "[", RowBox[List["a", "+", RowBox[List["c", " ", RowBox[List["Cosh", "[", RowBox[List["e", " ", "z"]], "]"]]]], "+", RowBox[List["b", " ", RowBox[List["Sinh", "[", RowBox[List["e", " ", "z"]], "]"]]]]]], "]"]]]], "e"]]], RowBox[List[RowBox[List["(", RowBox[List[RowBox[List["-", "b"]], "+", "c"]], ")"]], " ", RowBox[List["(", RowBox[List["b", "+", "c"]], ")"]]]]]]]]]


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





2002-12-18