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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/01.10.21.0044.01









  


  










Input Form





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










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





2002-12-18





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