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Coth




Mathematica Notation

Traditional Notation









Elementary Functions > Coth[z] > Integration > Indefinite integration > Involving functions of the direct function > Involving algebraic functions of the direct function > Involving ((a+b coth2(c z))n)beta





http://functions.wolfram.com/01.22.21.0280.01









  


  








Input Form





Integrate[Coth[c z]/Sqrt[(a + b Coth[c z]^2)^3], z] == -((-a + b + (a + b) Cosh[2 c z]) Csch[c z]^4 (-a - b + (a + b) Cosh[2 c z] - Sqrt[2] Sqrt[-a + b + (a + b) Cosh[2 c z]] Log[Sqrt[-a + b + (a + b) Cosh[2 c z]] + Sqrt[2] Sqrt[(a + b) Sinh[c z]^2]] Sqrt[(a + b) Sinh[c z]^2]))/ (4 (a + b)^2 c Sqrt[(a + b Coth[c z]^2)^3])








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[RowBox[List["Coth", "[", RowBox[List["c_", " ", "z_"]], "]"]], SqrtBox[SuperscriptBox[RowBox[List["(", RowBox[List["a_", "+", RowBox[List["b_", " ", SuperscriptBox[RowBox[List["Coth", "[", RowBox[List["c_", " ", "z_"]], "]"]], "2"]]]]], ")"]], "3"]]], RowBox[List["\[DifferentialD]", "z_"]]]]]], "]"]], "\[RuleDelayed]", RowBox[List["-", FractionBox[RowBox[List[RowBox[List["(", RowBox[List[RowBox[List["-", "a"]], "+", "b", "+", RowBox[List[RowBox[List["(", RowBox[List["a", "+", "b"]], ")"]], " ", RowBox[List["Cosh", "[", RowBox[List["2", " ", "c", " ", "z"]], "]"]]]]]], ")"]], " ", SuperscriptBox[RowBox[List["Csch", "[", RowBox[List["c", " ", "z"]], "]"]], "4"], " ", RowBox[List["(", RowBox[List[RowBox[List["-", "a"]], "-", "b", "+", RowBox[List[RowBox[List["(", RowBox[List["a", "+", "b"]], ")"]], " ", RowBox[List["Cosh", "[", RowBox[List["2", " ", "c", " ", "z"]], "]"]]]], "-", RowBox[List[SqrtBox["2"], " ", SqrtBox[RowBox[List[RowBox[List["-", "a"]], "+", "b", "+", RowBox[List[RowBox[List["(", RowBox[List["a", "+", "b"]], ")"]], " ", RowBox[List["Cosh", "[", RowBox[List["2", " ", "c", " ", "z"]], "]"]]]]]]], " ", RowBox[List["Log", "[", RowBox[List[SqrtBox[RowBox[List[RowBox[List["-", "a"]], "+", "b", "+", RowBox[List[RowBox[List["(", RowBox[List["a", "+", "b"]], ")"]], " ", RowBox[List["Cosh", "[", RowBox[List["2", " ", "c", " ", "z"]], "]"]]]]]]], "+", RowBox[List[SqrtBox["2"], " ", SqrtBox[RowBox[List[RowBox[List["(", RowBox[List["a", "+", "b"]], ")"]], " ", SuperscriptBox[RowBox[List["Sinh", "[", RowBox[List["c", " ", "z"]], "]"]], "2"]]]]]]]], "]"]], " ", SqrtBox[RowBox[List[RowBox[List["(", RowBox[List["a", "+", "b"]], ")"]], " ", SuperscriptBox[RowBox[List["Sinh", "[", RowBox[List["c", " ", "z"]], "]"]], "2"]]]]]]]], ")"]]]], RowBox[List["4", " ", SuperscriptBox[RowBox[List["(", RowBox[List["a", "+", "b"]], ")"]], "2"], " ", "c", " ", SqrtBox[SuperscriptBox[RowBox[List["(", RowBox[List["a", "+", RowBox[List["b", " ", SuperscriptBox[RowBox[List["Coth", "[", RowBox[List["c", " ", "z"]], "]"]], "2"]]]]], ")"]], "3"]]]]]]]]]]]


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





2002-12-18