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Csch






Mathematica Notation

Traditional Notation









Elementary Functions > Csch[z] > Integration > Indefinite integration > Involving one direct function and elementary functions > Involving hyperbolic functions > Involving sinh > Involving sinh(b z)





http://functions.wolfram.com/01.23.21.0075.01









  


  










Input Form





Integrate[Sinh[b z] Csch[c z], z] == (1/((c - b) (c + b))) (E^((c - b) z) ((c + b) Hypergeometric2F1[(c - b)/(2 c), 1, 3/2 - b/(2 c), E^(2 c z)] - (c - b) E^(2 b z) Hypergeometric2F1[(c + b)/(2 c), 1, (3 c + b)/(2 c), E^(2 c 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[RowBox[List["Sinh", "[", RowBox[List["b_", " ", "z_"]], "]"]], " ", RowBox[List["Csch", "[", RowBox[List["c_", " ", "z_"]], "]"]]]], RowBox[List["\[DifferentialD]", "z_"]]]]]], "]"]], "\[RuleDelayed]", FractionBox[RowBox[List[SuperscriptBox["\[ExponentialE]", RowBox[List[RowBox[List["(", RowBox[List["c", "-", "b"]], ")"]], " ", "z"]]], " ", RowBox[List["(", RowBox[List[RowBox[List[RowBox[List["(", RowBox[List["c", "+", "b"]], ")"]], " ", RowBox[List["Hypergeometric2F1", "[", RowBox[List[FractionBox[RowBox[List["c", "-", "b"]], RowBox[List["2", " ", "c"]]], ",", "1", ",", RowBox[List[FractionBox["3", "2"], "-", FractionBox["b", RowBox[List["2", " ", "c"]]]]], ",", SuperscriptBox["\[ExponentialE]", RowBox[List["2", " ", "c", " ", "z"]]]]], "]"]]]], "-", RowBox[List[RowBox[List["(", RowBox[List["c", "-", "b"]], ")"]], " ", SuperscriptBox["\[ExponentialE]", RowBox[List["2", " ", "b", " ", "z"]]], " ", RowBox[List["Hypergeometric2F1", "[", RowBox[List[FractionBox[RowBox[List["c", "+", "b"]], RowBox[List["2", " ", "c"]]], ",", "1", ",", FractionBox[RowBox[List[RowBox[List["3", " ", "c"]], "+", "b"]], RowBox[List["2", " ", "c"]]], ",", SuperscriptBox["\[ExponentialE]", RowBox[List["2", " ", "c", " ", "z"]]]]], "]"]]]]]], ")"]]]], RowBox[List[RowBox[List["(", RowBox[List["c", "-", "b"]], ")"]], " ", RowBox[List["(", RowBox[List["c", "+", "b"]], ")"]]]]]]]]]










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





2002-12-18