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Csc




Mathematica Notation

Traditional Notation









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





http://functions.wolfram.com/01.10.21.0043.01









  


  








Input Form





Integrate[Csc[ArcSinh[z]], z] == (1/2) E^((-1 + I) ArcSinh[z]) ((-1 - I) E^(2 ArcSinh[z]) Hypergeometric2F1[1/2 - I/2, 1, 3/2 - I/2, E^(2 I ArcSinh[z])] - (1 - I) Hypergeometric2F1[1/2 + I/2, 1, 3/2 + I/2, E^(2 I ArcSinh[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["Csc", "[", RowBox[List["ArcSinh", "[", "z_", "]"]], "]"]], RowBox[List["\[DifferentialD]", "z_"]]]]]], "]"]], "\[RuleDelayed]", RowBox[List[FractionBox["1", "2"], " ", SuperscriptBox["\[ExponentialE]", RowBox[List[RowBox[List["(", RowBox[List[RowBox[List["-", "1"]], "+", "\[ImaginaryI]"]], ")"]], " ", RowBox[List["ArcSinh", "[", "z", "]"]]]]], " ", RowBox[List["(", RowBox[List[RowBox[List[RowBox[List["(", RowBox[List[RowBox[List["-", "1"]], "-", "\[ImaginaryI]"]], ")"]], " ", SuperscriptBox["\[ExponentialE]", RowBox[List["2", " ", RowBox[List["ArcSinh", "[", "z", "]"]]]]], " ", RowBox[List["Hypergeometric2F1", "[", RowBox[List[RowBox[List[FractionBox["1", "2"], "-", FractionBox["\[ImaginaryI]", "2"]]], ",", "1", ",", RowBox[List[FractionBox["3", "2"], "-", FractionBox["\[ImaginaryI]", "2"]]], ",", SuperscriptBox["\[ExponentialE]", RowBox[List["2", " ", "\[ImaginaryI]", " ", RowBox[List["ArcSinh", "[", "z", "]"]]]]]]], "]"]]]], "-", RowBox[List[RowBox[List["(", RowBox[List["1", "-", "\[ImaginaryI]"]], ")"]], " ", RowBox[List["Hypergeometric2F1", "[", RowBox[List[RowBox[List[FractionBox["1", "2"], "+", FractionBox["\[ImaginaryI]", "2"]]], ",", "1", ",", RowBox[List[FractionBox["3", "2"], "+", FractionBox["\[ImaginaryI]", "2"]]], ",", SuperscriptBox["\[ExponentialE]", RowBox[List["2", " ", "\[ImaginaryI]", " ", RowBox[List["ArcSinh", "[", "z", "]"]]]]]]], "]"]]]]]], ")"]]]]]]]]


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





2002-12-18