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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 +b sinh2(e z)+c cosh2(e z))beta





http://functions.wolfram.com/01.20.21.4430.01









  


  








Input Form





Integrate[Sqrt[a + b Sinh[e z]^2 + c Cosh[e z]^2], z] == (-I) Cosh[e z] EllipticE[I ArcSinh[Sinh[e z]], (b + c)/(a + c)] (Sqrt[a + c + (b + c) Sinh[e z]^2]/(e Sqrt[Cosh[e z]^2] Sqrt[(a + c + (b + c) Sinh[e z]^2)/(a + c)]))








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[SqrtBox[RowBox[List["a_", "+", RowBox[List["b_", " ", SuperscriptBox[RowBox[List["Sinh", "[", RowBox[List["e_", " ", "z_"]], "]"]], "2"]]], "+", RowBox[List["c_", " ", SuperscriptBox[RowBox[List["Cosh", "[", RowBox[List["e_", " ", "z_"]], "]"]], "2"]]]]]], RowBox[List["\[DifferentialD]", "z_"]]]]]], "]"]], "\[RuleDelayed]", RowBox[List["-", FractionBox[RowBox[List["\[ImaginaryI]", " ", RowBox[List["Cosh", "[", RowBox[List["e", " ", "z"]], "]"]], " ", RowBox[List["EllipticE", "[", RowBox[List[RowBox[List["\[ImaginaryI]", " ", RowBox[List["ArcSinh", "[", RowBox[List["Sinh", "[", RowBox[List["e", " ", "z"]], "]"]], "]"]]]], ",", FractionBox[RowBox[List["b", "+", "c"]], RowBox[List["a", "+", "c"]]]]], "]"]], " ", SqrtBox[RowBox[List["a", "+", "c", "+", RowBox[List[RowBox[List["(", RowBox[List["b", "+", "c"]], ")"]], " ", SuperscriptBox[RowBox[List["Sinh", "[", RowBox[List["e", " ", "z"]], "]"]], "2"]]]]]]]], RowBox[List["e", " ", SqrtBox[SuperscriptBox[RowBox[List["Cosh", "[", RowBox[List["e", " ", "z"]], "]"]], "2"]], " ", SqrtBox[FractionBox[RowBox[List["a", "+", "c", "+", RowBox[List[RowBox[List["(", RowBox[List["b", "+", "c"]], ")"]], " ", SuperscriptBox[RowBox[List["Sinh", "[", RowBox[List["e", " ", "z"]], "]"]], "2"]]]]], RowBox[List["a", "+", "c"]]]]]]]]]]]]]


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





2002-12-18