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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 sinh > Involving sinhm(c z)coshm(c z)(a+b cosh(2c z))beta





http://functions.wolfram.com/01.20.21.4374.01









  


  










Input Form





Integrate[(Sinh[c z]^3 Cosh[c z]^4)/(a + b Cosh[2 c z])^(3/2), z] == (Sqrt[b] (-30 a^2 - 3 a b + 19 b^2) Cosh[c z] + b^(3/2) (-5 a + 2 b) Cosh[3 c z] + b^(5/2) Cosh[5 c z] + 15 Sqrt[2] a^2 Sqrt[a + b Cosh[2 c z]] Log[Sqrt[2] Sqrt[b] Cosh[c z] + Sqrt[a + b Cosh[2 c z]]] - 6 Sqrt[2] a b Sqrt[a + b Cosh[2 c z]] Log[Sqrt[2] Sqrt[b] Cosh[c z] + Sqrt[a + b Cosh[2 c z]]] - 9 Sqrt[2] b^2 Sqrt[a + b Cosh[2 c z]] Log[Sqrt[2] Sqrt[b] Cosh[c z] + Sqrt[a + b Cosh[2 c z]]])/ (128 b^(7/2) c Sqrt[a + b Cosh[2 c z]])










Standard Form





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MathML Form







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</semantics> </math>










Rule Form





Cell[BoxData[RowBox[List[RowBox[List["HoldPattern", "[", RowBox[List["\[Integral]", RowBox[List[FractionBox[RowBox[List[SuperscriptBox[RowBox[List["Sinh", "[", RowBox[List["c_", " ", "z_"]], "]"]], "3"], " ", SuperscriptBox[RowBox[List["Cosh", "[", RowBox[List["c_", " ", "z_"]], "]"]], "4"]]], SuperscriptBox[RowBox[List["(", RowBox[List["a_", "+", RowBox[List["b_", " ", RowBox[List["Cosh", "[", RowBox[List["2", " ", "c_", " ", "z_"]], "]"]]]]]], ")"]], RowBox[List["3", "/", "2"]]]], RowBox[List["\[DifferentialD]", "z_"]]]]]], "]"]], "\[RuleDelayed]", FractionBox[RowBox[List[RowBox[List[SqrtBox["b"], " ", RowBox[List["(", RowBox[List[RowBox[List[RowBox[List["-", "30"]], " ", SuperscriptBox["a", "2"]]], "-", RowBox[List["3", " ", "a", " ", "b"]], "+", RowBox[List["19", " ", SuperscriptBox["b", "2"]]]]], ")"]], " ", RowBox[List["Cosh", "[", RowBox[List["c", " ", "z"]], "]"]]]], "+", RowBox[List[SuperscriptBox["b", RowBox[List["3", "/", "2"]]], " ", RowBox[List["(", RowBox[List[RowBox[List[RowBox[List["-", "5"]], " ", "a"]], "+", RowBox[List["2", " ", "b"]]]], ")"]], " ", RowBox[List["Cosh", "[", RowBox[List["3", " ", "c", " ", "z"]], "]"]]]], "+", RowBox[List[SuperscriptBox["b", RowBox[List["5", "/", "2"]]], " ", RowBox[List["Cosh", "[", RowBox[List["5", " ", "c", " ", "z"]], "]"]]]], "+", RowBox[List["15", " ", SqrtBox["2"], " ", SuperscriptBox["a", "2"], " ", SqrtBox[RowBox[List["a", "+", RowBox[List["b", " ", RowBox[List["Cosh", "[", RowBox[List["2", " ", "c", " ", "z"]], "]"]]]]]]], " ", RowBox[List["Log", "[", RowBox[List[RowBox[List[SqrtBox["2"], " ", SqrtBox["b"], " ", RowBox[List["Cosh", "[", RowBox[List["c", " ", "z"]], "]"]]]], "+", SqrtBox[RowBox[List["a", "+", RowBox[List["b", " ", RowBox[List["Cosh", "[", RowBox[List["2", " ", "c", " ", "z"]], "]"]]]]]]]]], "]"]]]], "-", RowBox[List["6", " ", SqrtBox["2"], " ", "a", " ", "b", " ", SqrtBox[RowBox[List["a", "+", RowBox[List["b", " ", RowBox[List["Cosh", "[", RowBox[List["2", " ", "c", " ", "z"]], "]"]]]]]]], " ", RowBox[List["Log", "[", RowBox[List[RowBox[List[SqrtBox["2"], " ", SqrtBox["b"], " ", RowBox[List["Cosh", "[", RowBox[List["c", " ", "z"]], "]"]]]], "+", SqrtBox[RowBox[List["a", "+", RowBox[List["b", " ", RowBox[List["Cosh", "[", RowBox[List["2", " ", "c", " ", "z"]], "]"]]]]]]]]], "]"]]]], "-", RowBox[List["9", " ", SqrtBox["2"], " ", SuperscriptBox["b", "2"], " ", SqrtBox[RowBox[List["a", "+", RowBox[List["b", " ", RowBox[List["Cosh", "[", RowBox[List["2", " ", "c", " ", "z"]], "]"]]]]]]], " ", RowBox[List["Log", "[", RowBox[List[RowBox[List[SqrtBox["2"], " ", SqrtBox["b"], " ", RowBox[List["Cosh", "[", RowBox[List["c", " ", "z"]], "]"]]]], "+", SqrtBox[RowBox[List["a", "+", RowBox[List["b", " ", RowBox[List["Cosh", "[", RowBox[List["2", " ", "c", " ", "z"]], "]"]]]]]]]]], "]"]]]]]], RowBox[List["128", " ", SuperscriptBox["b", RowBox[List["7", "/", "2"]]], " ", "c", " ", SqrtBox[RowBox[List["a", "+", RowBox[List["b", " ", RowBox[List["Cosh", "[", RowBox[List["2", " ", "c", " ", "z"]], "]"]]]]]]]]]]]]]]










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





2002-12-18