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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 sinh(2c z))beta sinhv(c z)





http://functions.wolfram.com/01.19.21.1755.01









  


  










Input Form





Integrate[Sinh[c z]^2/Sqrt[a + b Sinh[2 c z]], z] == ((-I) b EllipticF[(1/4) (Pi - 4 I c z), -((2 I b)/(a - I b))] Sqrt[(a + b Sinh[2 c z])/(a - I b)] + 2 Cosh[(c z)/2]^4 Sqrt[(a + b Sinh[2 c z])/(1 + Cosh[c z])^2] Sqrt[Sech[(c z)/2]^4 (a + b Sinh[2 c z])])/(2 b c Sqrt[a + b Sinh[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_"]], "]"]], "2"], SqrtBox[RowBox[List["a_", "+", RowBox[List["b_", " ", RowBox[List["Sinh", "[", RowBox[List["2", " ", "c_", " ", "z_"]], "]"]]]]]]]], RowBox[List["\[DifferentialD]", "z_"]]]]]], "]"]], "\[RuleDelayed]", FractionBox[RowBox[List[RowBox[List[RowBox[List["-", "\[ImaginaryI]"]], " ", "b", " ", RowBox[List["EllipticF", "[", RowBox[List[RowBox[List[FractionBox["1", "4"], " ", RowBox[List["(", RowBox[List["\[Pi]", "-", RowBox[List["4", " ", "\[ImaginaryI]", " ", "c", " ", "z"]]]], ")"]]]], ",", RowBox[List["-", FractionBox[RowBox[List["2", " ", "\[ImaginaryI]", " ", "b"]], RowBox[List["a", "-", RowBox[List["\[ImaginaryI]", " ", "b"]]]]]]]]], "]"]], " ", SqrtBox[FractionBox[RowBox[List["a", "+", RowBox[List["b", " ", RowBox[List["Sinh", "[", RowBox[List["2", " ", "c", " ", "z"]], "]"]]]]]], RowBox[List["a", "-", RowBox[List["\[ImaginaryI]", " ", "b"]]]]]]]], "+", RowBox[List["2", " ", SuperscriptBox[RowBox[List["Cosh", "[", FractionBox[RowBox[List["c", " ", "z"]], "2"], "]"]], "4"], " ", SqrtBox[FractionBox[RowBox[List["a", "+", RowBox[List["b", " ", RowBox[List["Sinh", "[", RowBox[List["2", " ", "c", " ", "z"]], "]"]]]]]], SuperscriptBox[RowBox[List["(", RowBox[List["1", "+", RowBox[List["Cosh", "[", RowBox[List["c", " ", "z"]], "]"]]]], ")"]], "2"]]], " ", SqrtBox[RowBox[List[SuperscriptBox[RowBox[List["Sech", "[", FractionBox[RowBox[List["c", " ", "z"]], "2"], "]"]], "4"], " ", RowBox[List["(", RowBox[List["a", "+", RowBox[List["b", " ", RowBox[List["Sinh", "[", RowBox[List["2", " ", "c", " ", "z"]], "]"]]]]]], ")"]]]]]]]]], RowBox[List["2", " ", "b", " ", "c", " ", SqrtBox[RowBox[List["a", "+", RowBox[List["b", " ", RowBox[List["Sinh", "[", RowBox[List["2", " ", "c", " ", "z"]], "]"]]]]]]]]]]]]]]










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





2002-12-18