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Csch




Mathematica Notation

Traditional Notation









Elementary Functions > Csch[z] > Integration > Indefinite integration > Involving one direct function and elementary functions > Arguments involving inverse hyperbolic functions > Involving cosh-1





http://functions.wolfram.com/01.23.21.0042.01









  


  








Input Form





Integrate[Csch[a ArcCosh[z]], z] == (1/(-1 + a^2)) (((1 + a) E^(a ArcCosh[z]) Hypergeometric2F1[(-1 + a)/(2 a), 1, 3/2 - 1/(2 a), E^(2 a ArcCosh[z])] - (-1 + a) E^((2 + a) ArcCosh[z]) Hypergeometric2F1[(1 + a)/(2 a), 1, (1/2) (3 + 1/a), E^(2 a ArcCosh[z])])/E^ArcCosh[z])








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["Csch", "[", RowBox[List["a_", " ", RowBox[List["ArcCosh", "[", "z_", "]"]]]], "]"]], RowBox[List["\[DifferentialD]", "z_"]]]]]], "]"]], "\[RuleDelayed]", FractionBox[RowBox[List[SuperscriptBox["\[ExponentialE]", RowBox[List["-", RowBox[List["ArcCosh", "[", "z", "]"]]]]], " ", RowBox[List["(", RowBox[List[RowBox[List[RowBox[List["(", RowBox[List["1", "+", "a"]], ")"]], " ", SuperscriptBox["\[ExponentialE]", RowBox[List["a", " ", RowBox[List["ArcCosh", "[", "z", "]"]]]]], " ", RowBox[List["Hypergeometric2F1", "[", RowBox[List[FractionBox[RowBox[List[RowBox[List["-", "1"]], "+", "a"]], RowBox[List["2", " ", "a"]]], ",", "1", ",", RowBox[List[FractionBox["3", "2"], "-", FractionBox["1", RowBox[List["2", " ", "a"]]]]], ",", SuperscriptBox["\[ExponentialE]", RowBox[List["2", " ", "a", " ", RowBox[List["ArcCosh", "[", "z", "]"]]]]]]], "]"]]]], "-", RowBox[List[RowBox[List["(", RowBox[List[RowBox[List["-", "1"]], "+", "a"]], ")"]], " ", SuperscriptBox["\[ExponentialE]", RowBox[List[RowBox[List["(", RowBox[List["2", "+", "a"]], ")"]], " ", RowBox[List["ArcCosh", "[", "z", "]"]]]]], " ", RowBox[List["Hypergeometric2F1", "[", RowBox[List[FractionBox[RowBox[List["1", "+", "a"]], RowBox[List["2", " ", "a"]]], ",", "1", ",", RowBox[List[FractionBox["1", "2"], " ", RowBox[List["(", RowBox[List["3", "+", FractionBox["1", "a"]]], ")"]]]], ",", SuperscriptBox["\[ExponentialE]", RowBox[List["2", " ", "a", " ", RowBox[List["ArcCosh", "[", "z", "]"]]]]]]], "]"]]]]]], ")"]]]], RowBox[List[RowBox[List["-", "1"]], "+", SuperscriptBox["a", "2"]]]]]]]]


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





2002-12-18