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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 sinh(e z)+b cosh(e z))beta





http://functions.wolfram.com/01.20.21.4396.01









  


  








Input Form





Integrate[Sinh[e z]/Sqrt[a Sinh[e z] + b Cosh[e z]], z] == (a HypergeometricPFQ[{-(1/2), -(1/4)}, {3/4}, Cosh[e z + ArcTanh[a/b]]^2] Sinh[e z + ArcTanh[a/b]] + Sqrt[-Sinh[e z + ArcTanh[a/b]]^2] (2 b Cosh[e z + ArcTanh[a/b]] - a Sinh[e z + ArcTanh[a/b]]))/ (Sqrt[1 - a^2/b^2] b e Sqrt[b Cosh[e z] + a Sinh[e z]] Sqrt[-Sinh[e z + ArcTanh[a/b]]^2])








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["Sinh", "[", RowBox[List["e_", " ", "z_"]], "]"]], SqrtBox[RowBox[List[RowBox[List["a_", " ", 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[RowBox[List["a", " ", RowBox[List["HypergeometricPFQ", "[", RowBox[List[RowBox[List["{", RowBox[List[RowBox[List["-", FractionBox["1", "2"]]], ",", RowBox[List["-", FractionBox["1", "4"]]]]], "}"]], ",", RowBox[List["{", FractionBox["3", "4"], "}"]], ",", SuperscriptBox[RowBox[List["Cosh", "[", RowBox[List[RowBox[List["e", " ", "z"]], "+", RowBox[List["ArcTanh", "[", FractionBox["a", "b"], "]"]]]], "]"]], "2"]]], "]"]], " ", RowBox[List["Sinh", "[", RowBox[List[RowBox[List["e", " ", "z"]], "+", RowBox[List["ArcTanh", "[", FractionBox["a", "b"], "]"]]]], "]"]]]], "+", RowBox[List[SqrtBox[RowBox[List["-", SuperscriptBox[RowBox[List["Sinh", "[", RowBox[List[RowBox[List["e", " ", "z"]], "+", RowBox[List["ArcTanh", "[", FractionBox["a", "b"], "]"]]]], "]"]], "2"]]]], " ", RowBox[List["(", RowBox[List[RowBox[List["2", " ", "b", " ", RowBox[List["Cosh", "[", RowBox[List[RowBox[List["e", " ", "z"]], "+", RowBox[List["ArcTanh", "[", FractionBox["a", "b"], "]"]]]], "]"]]]], "-", RowBox[List["a", " ", RowBox[List["Sinh", "[", RowBox[List[RowBox[List["e", " ", "z"]], "+", RowBox[List["ArcTanh", "[", FractionBox["a", "b"], "]"]]]], "]"]]]]]], ")"]]]]]], RowBox[List[SqrtBox[RowBox[List["1", "-", FractionBox[SuperscriptBox["a", "2"], SuperscriptBox["b", "2"]]]]], " ", "b", " ", "e", " ", SqrtBox[RowBox[List[RowBox[List["b", " ", RowBox[List["Cosh", "[", RowBox[List["e", " ", "z"]], "]"]]]], "+", RowBox[List["a", " ", RowBox[List["Sinh", "[", RowBox[List["e", " ", "z"]], "]"]]]]]]], " ", SqrtBox[RowBox[List["-", SuperscriptBox[RowBox[List["Sinh", "[", RowBox[List[RowBox[List["e", " ", "z"]], "+", RowBox[List["ArcTanh", "[", FractionBox["a", "b"], "]"]]]], "]"]], "2"]]]]]]]]]]]


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





2002-12-18