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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/01.20.21.4278.01









  


  










Input Form





Integrate[(A + B Sinh[e z] + C Cosh[e z])/(b Sinh[e z] + c Cosh[e z]), z] == -(2 A (b - c) Sqrt[b + c] ArcTan[(b + c Tanh[(e z)/2])/ (Sqrt[-b + c] Sqrt[b + c])] + Sqrt[-b + c] ((b B - c C) e z + ((-B) c + b C) Log[c Cosh[e z] + b Sinh[e z]]))/ ((-b + c)^(3/2) (b + c) 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[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]", RowBox[List["-", FractionBox[RowBox[List[RowBox[List["2", " ", "A", " ", RowBox[List["(", RowBox[List["b", "-", "c"]], ")"]], " ", SqrtBox[RowBox[List["b", "+", "c"]]], " ", RowBox[List["ArcTan", "[", FractionBox[RowBox[List["b", "+", RowBox[List["c", " ", RowBox[List["Tanh", "[", FractionBox[RowBox[List["e", " ", "z"]], "2"], "]"]]]]]], RowBox[List[SqrtBox[RowBox[List[RowBox[List["-", "b"]], "+", "c"]]], " ", SqrtBox[RowBox[List["b", "+", "c"]]]]]], "]"]]]], "+", RowBox[List[SqrtBox[RowBox[List[RowBox[List["-", "b"]], "+", "c"]]], " ", RowBox[List["(", RowBox[List[RowBox[List[RowBox[List["(", RowBox[List[RowBox[List["b", " ", "B"]], "-", RowBox[List["c", " ", "C"]]]], ")"]], " ", "e", " ", "z"]], "+", RowBox[List[RowBox[List["(", RowBox[List[RowBox[List[RowBox[List["-", "B"]], " ", "c"]], "+", RowBox[List["b", " ", "C"]]]], ")"]], " ", RowBox[List["Log", "[", RowBox[List[RowBox[List["c", " ", RowBox[List["Cosh", "[", RowBox[List["e", " ", "z"]], "]"]]]], "+", RowBox[List["b", " ", RowBox[List["Sinh", "[", RowBox[List["e", " ", "z"]], "]"]]]]]], "]"]]]]]], ")"]]]]]], RowBox[List[SuperscriptBox[RowBox[List["(", RowBox[List[RowBox[List["-", "b"]], "+", "c"]], ")"]], RowBox[List["3", "/", "2"]]], " ", RowBox[List["(", RowBox[List["b", "+", "c"]], ")"]], " ", "e"]]]]]]]]]










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





2002-12-18