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Tanh






Mathematica Notation

Traditional Notation









Elementary Functions > Tanh[z] > Integration > Indefinite integration > Involving functions of the direct function and hyperbolic functions > Involving algebraic functions of the direct function and hyperbolic functions > Involving cosh > Involving cosh(c z)(a+b tanh2(c z))beta





http://functions.wolfram.com/01.21.21.0363.01









  


  










Input Form





Integrate[Cosh[c z] (a + b Tanh[c z]^2)^\[Beta], z] == (1/c) ((AppellF1[1/2, 3/2, -\[Beta], 3/2, Tanh[c z]^2, -((b Tanh[c z]^2)/a)] Sqrt[Sech[c z]^2] Sinh[c z] (a + b Tanh[c z]^2)^\[Beta])/ (1 + (b Tanh[c z]^2)/a)^\[Beta])










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["c_", " ", "z_"]], "]"]], " ", SuperscriptBox[RowBox[List["(", RowBox[List["a_", "+", RowBox[List["b_", " ", SuperscriptBox[RowBox[List["Tanh", "[", RowBox[List["c_", " ", "z_"]], "]"]], "2"]]]]], ")"]], "\[Beta]_"]]], RowBox[List["\[DifferentialD]", "z_"]]]]]], "]"]], "\[RuleDelayed]", FractionBox[RowBox[List[RowBox[List["AppellF1", "[", RowBox[List[FractionBox["1", "2"], ",", FractionBox["3", "2"], ",", RowBox[List["-", "\[Beta]"]], ",", FractionBox["3", "2"], ",", SuperscriptBox[RowBox[List["Tanh", "[", RowBox[List["c", " ", "z"]], "]"]], "2"], ",", RowBox[List["-", FractionBox[RowBox[List["b", " ", SuperscriptBox[RowBox[List["Tanh", "[", RowBox[List["c", " ", "z"]], "]"]], "2"]]], "a"]]]]], "]"]], " ", SqrtBox[SuperscriptBox[RowBox[List["Sech", "[", RowBox[List["c", " ", "z"]], "]"]], "2"]], " ", RowBox[List["Sinh", "[", RowBox[List["c", " ", "z"]], "]"]], " ", SuperscriptBox[RowBox[List["(", RowBox[List["a", "+", RowBox[List["b", " ", SuperscriptBox[RowBox[List["Tanh", "[", RowBox[List["c", " ", "z"]], "]"]], "2"]]]]], ")"]], "\[Beta]"], " ", SuperscriptBox[RowBox[List["(", RowBox[List["1", "+", FractionBox[RowBox[List["b", " ", SuperscriptBox[RowBox[List["Tanh", "[", RowBox[List["c", " ", "z"]], "]"]], "2"]]], "a"]]], ")"]], RowBox[List["-", "\[Beta]"]]]]], "c"]]]]]










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





2002-12-18