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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/01.20.21.4279.01









  


  










Input Form





Integrate[(A + B Sinh[e z] + C Cosh[e z])/(a + b Sinh[e z] + b Cosh[e z]), z] == (1/(4 a^2 b e)) ((2 a b (B - C) + E^(e z) ((2 a A b + b^2 (B - C) + a^2 (B + C)) e z + 2 (-2 a A b + b^2 (-B + C) + a^2 (B + C)) Log[(a + b E^(e z))/E^((e z)/2)]))/E^(e 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["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["b_", " ", RowBox[List["Cosh", "[", RowBox[List["e_", " ", "z_"]], "]"]]]]]]], RowBox[List["\[DifferentialD]", "z_"]]]]]], "]"]], "\[RuleDelayed]", FractionBox[RowBox[List[SuperscriptBox["\[ExponentialE]", RowBox[List[RowBox[List["-", "e"]], " ", "z"]]], " ", RowBox[List["(", RowBox[List[RowBox[List["2", " ", "a", " ", "b", " ", RowBox[List["(", RowBox[List["B", "-", "C"]], ")"]]]], "+", RowBox[List[SuperscriptBox["\[ExponentialE]", RowBox[List["e", " ", "z"]]], " ", RowBox[List["(", RowBox[List[RowBox[List[RowBox[List["(", RowBox[List[RowBox[List["2", " ", "a", " ", "A", " ", "b"]], "+", RowBox[List[SuperscriptBox["b", "2"], " ", RowBox[List["(", RowBox[List["B", "-", "C"]], ")"]]]], "+", RowBox[List[SuperscriptBox["a", "2"], " ", RowBox[List["(", RowBox[List["B", "+", "C"]], ")"]]]]]], ")"]], " ", "e", " ", "z"]], "+", RowBox[List["2", " ", RowBox[List["(", RowBox[List[RowBox[List[RowBox[List["-", "2"]], " ", "a", " ", "A", " ", "b"]], "+", RowBox[List[SuperscriptBox["b", "2"], " ", RowBox[List["(", RowBox[List[RowBox[List["-", "B"]], "+", "C"]], ")"]]]], "+", RowBox[List[SuperscriptBox["a", "2"], " ", RowBox[List["(", RowBox[List["B", "+", "C"]], ")"]]]]]], ")"]], " ", RowBox[List["Log", "[", RowBox[List[SuperscriptBox["\[ExponentialE]", RowBox[List[RowBox[List["-", FractionBox["1", "2"]]], " ", RowBox[List["(", RowBox[List["e", " ", "z"]], ")"]]]]], " ", RowBox[List["(", RowBox[List["a", "+", RowBox[List["b", " ", SuperscriptBox["\[ExponentialE]", RowBox[List["e", " ", "z"]]]]]]], ")"]]]], "]"]]]]]], ")"]]]]]], ")"]]]], RowBox[List["4", " ", SuperscriptBox["a", "2"], " ", "b", " ", "e"]]]]]]]










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





2002-12-18