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Sinh






Mathematica Notation

Traditional Notation









Elementary Functions > Sinh[z] > Integration > Indefinite integration > Involving functions of the direct function > Involving algebraic functions of the direct function > Involving (a+b sinh2(c z))beta sinhnu(c z)





http://functions.wolfram.com/01.19.21.1811.01









  


  










Input Form





Integrate[Sinh[c z]^4/(a + b Sinh[c z]^2)^(3/2), z] == -(I a (2 (2 a - b) Sqrt[(2 a - b + b Cosh[2 c z])/a] EllipticE[I c z, b/a] - 4 (a - b) Sqrt[(2 a - b + b Cosh[2 c z])/a] EllipticF[I c z, b/a] - I Sqrt[2] b Sinh[2 c z]))/(2 (a - b) b^2 c Sqrt[2 a - b + b Cosh[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[FractionBox[SuperscriptBox[RowBox[List["Sinh", "[", RowBox[List["c_", " ", "z_"]], "]"]], "4"], SuperscriptBox[RowBox[List["(", RowBox[List["a_", "+", RowBox[List["b_", " ", SuperscriptBox[RowBox[List["Sinh", "[", RowBox[List["c_", " ", "z_"]], "]"]], "2"]]]]], ")"]], RowBox[List["3", "/", "2"]]]], RowBox[List["\[DifferentialD]", "z_"]]]]]], "]"]], "\[RuleDelayed]", RowBox[List["-", FractionBox[RowBox[List["\[ImaginaryI]", " ", "a", " ", RowBox[List["(", RowBox[List[RowBox[List["2", " ", RowBox[List["(", RowBox[List[RowBox[List["2", " ", "a"]], "-", "b"]], ")"]], " ", SqrtBox[FractionBox[RowBox[List[RowBox[List["2", " ", "a"]], "-", "b", "+", RowBox[List["b", " ", RowBox[List["Cosh", "[", RowBox[List["2", " ", "c", " ", "z"]], "]"]]]]]], "a"]], " ", RowBox[List["EllipticE", "[", RowBox[List[RowBox[List["\[ImaginaryI]", " ", "c", " ", "z"]], ",", FractionBox["b", "a"]]], "]"]]]], "-", RowBox[List["4", " ", RowBox[List["(", RowBox[List["a", "-", "b"]], ")"]], " ", SqrtBox[FractionBox[RowBox[List[RowBox[List["2", " ", "a"]], "-", "b", "+", RowBox[List["b", " ", RowBox[List["Cosh", "[", RowBox[List["2", " ", "c", " ", "z"]], "]"]]]]]], "a"]], " ", RowBox[List["EllipticF", "[", RowBox[List[RowBox[List["\[ImaginaryI]", " ", "c", " ", "z"]], ",", FractionBox["b", "a"]]], "]"]]]], "-", RowBox[List["\[ImaginaryI]", " ", SqrtBox["2"], " ", "b", " ", RowBox[List["Sinh", "[", RowBox[List["2", " ", "c", " ", "z"]], "]"]]]]]], ")"]]]], RowBox[List["2", " ", RowBox[List["(", RowBox[List["a", "-", "b"]], ")"]], " ", SuperscriptBox["b", "2"], " ", "c", " ", SqrtBox[RowBox[List[RowBox[List["2", " ", "a"]], "-", "b", "+", RowBox[List["b", " ", RowBox[List["Cosh", "[", RowBox[List["2", " ", "c", " ", "z"]], "]"]]]]]]]]]]]]]]]]










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





2002-12-18