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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 algebraic functions of the direct function and hyperbolic functions > Involving algebraic functions of sinh > Involving (a sinh2(e z)+b cosh2(e z))beta





http://functions.wolfram.com/01.20.21.4423.01









  


  










Input Form





Integrate[Cosh[e z] (a Sinh[e z]^2 + b Cosh[e z]^2)^\[Beta], z] == (-(-a + (a + b) Cosh[e z]^2)) Hypergeometric2F1[1 + \[Beta], 1/2, 2 + \[Beta], (-a + (a + b) Cosh[e z]^2)/b] Sinh[e z] ((b Cosh[e z]^2 + a Sinh[e z]^2)^\[Beta]/(2 b e (1 + \[Beta]) Sqrt[-(((a + b) Sinh[e z]^2)/b)]))










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[RowBox[List[RowBox[List["Cosh", "[", RowBox[List["e_", " ", "z_"]], "]"]], " ", SuperscriptBox[RowBox[List["(", RowBox[List[RowBox[List["a_", " ", SuperscriptBox[RowBox[List["Sinh", "[", RowBox[List["e_", " ", "z_"]], "]"]], "2"]]], "+", RowBox[List["b_", " ", SuperscriptBox[RowBox[List["Cosh", "[", RowBox[List["e_", " ", "z_"]], "]"]], "2"]]]]], ")"]], "\[Beta]_"]]], RowBox[List["\[DifferentialD]", "z_"]]]]]], "]"]], "\[RuleDelayed]", RowBox[List["-", FractionBox[RowBox[List[RowBox[List["(", RowBox[List[RowBox[List["-", "a"]], "+", RowBox[List[RowBox[List["(", RowBox[List["a", "+", "b"]], ")"]], " ", SuperscriptBox[RowBox[List["Cosh", "[", RowBox[List["e", " ", "z"]], "]"]], "2"]]]]], ")"]], " ", RowBox[List["Hypergeometric2F1", "[", RowBox[List[RowBox[List["1", "+", "\[Beta]"]], ",", FractionBox["1", "2"], ",", RowBox[List["2", "+", "\[Beta]"]], ",", FractionBox[RowBox[List[RowBox[List["-", "a"]], "+", RowBox[List[RowBox[List["(", RowBox[List["a", "+", "b"]], ")"]], " ", SuperscriptBox[RowBox[List["Cosh", "[", RowBox[List["e", " ", "z"]], "]"]], "2"]]]]], "b"]]], "]"]], " ", RowBox[List["Sinh", "[", RowBox[List["e", " ", "z"]], "]"]], " ", SuperscriptBox[RowBox[List["(", RowBox[List[RowBox[List["b", " ", SuperscriptBox[RowBox[List["Cosh", "[", RowBox[List["e", " ", "z"]], "]"]], "2"]]], "+", RowBox[List["a", " ", SuperscriptBox[RowBox[List["Sinh", "[", RowBox[List["e", " ", "z"]], "]"]], "2"]]]]], ")"]], "\[Beta]"]]], RowBox[List["2", " ", "b", " ", "e", " ", RowBox[List["(", RowBox[List["1", "+", "\[Beta]"]], ")"]], " ", SqrtBox[RowBox[List["-", FractionBox[RowBox[List[RowBox[List["(", RowBox[List["a", "+", "b"]], ")"]], " ", SuperscriptBox[RowBox[List["Sinh", "[", RowBox[List["e", " ", "z"]], "]"]], "2"]]], "b"]]]]]]]]]]]]]










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





2002-12-18