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Sinh




Mathematica Notation

Traditional Notation









Elementary Functions > Sinh[z] > Integration > Indefinite integration > Involving one direct function and elementary functions > Arguments involving inverse trigonometric functions > Involving sec-1





http://functions.wolfram.com/01.19.21.0436.01









  


  








Input Form





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


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





2002-12-18