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Sech






Mathematica Notation

Traditional Notation









Elementary Functions > Sech[z] > Integration > Indefinite integration > Involving one direct function and elementary functions > Involving hyperbolic and exponential functions > Involving power of cosh and exp > Involving ep zcoshm(b z)





http://functions.wolfram.com/01.24.21.0189.01









  


  










Input Form





Integrate[E^(c (\[Mu] - 1) z) Cosh[c z]^\[Mu] Sech[c z], z] == ((1/(c (-1 + \[Mu]))) E^(c z (-2 + \[Mu])) Cosh[c z]^\[Mu] Hypergeometric2F1[1 - \[Mu], 1 - \[Mu], 2 - \[Mu], -E^(-2 c z)])/ (1 + E^(-2 c z))^\[Mu]










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[SuperscriptBox["\[ExponentialE]", RowBox[List["c_", " ", RowBox[List["(", RowBox[List["\[Mu]_", "-", "1"]], ")"]], " ", "z_"]]], " ", SuperscriptBox[RowBox[List["Cosh", "[", RowBox[List["c_", " ", "z_"]], "]"]], "\[Mu]_"], " ", RowBox[List["Sech", "[", RowBox[List["c_", " ", "z_"]], "]"]]]], RowBox[List["\[DifferentialD]", "z_"]]]]]], "]"]], "\[RuleDelayed]", FractionBox[RowBox[List[SuperscriptBox["\[ExponentialE]", RowBox[List["c", " ", "z", " ", RowBox[List["(", RowBox[List[RowBox[List["-", "2"]], "+", "\[Mu]"]], ")"]]]]], " ", SuperscriptBox[RowBox[List["(", RowBox[List["1", "+", SuperscriptBox["\[ExponentialE]", RowBox[List[RowBox[List["-", "2"]], " ", "c", " ", "z"]]]]], ")"]], RowBox[List["-", "\[Mu]"]]], " ", SuperscriptBox[RowBox[List["Cosh", "[", RowBox[List["c", " ", "z"]], "]"]], "\[Mu]"], " ", RowBox[List["Hypergeometric2F1", "[", RowBox[List[RowBox[List["1", "-", "\[Mu]"]], ",", RowBox[List["1", "-", "\[Mu]"]], ",", RowBox[List["2", "-", "\[Mu]"]], ",", RowBox[List["-", SuperscriptBox["\[ExponentialE]", RowBox[List[RowBox[List["-", "2"]], " ", "c", " ", "z"]]]]]]], "]"]]]], RowBox[List["c", " ", RowBox[List["(", RowBox[List[RowBox[List["-", "1"]], "+", "\[Mu]"]], ")"]]]]]]]]]










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





2002-12-18





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