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Coth






Mathematica Notation

Traditional Notation









Elementary Functions > Coth[z] > Integration > Indefinite integration > Involving functions of the direct function and hyperbolic functions > Involving powers of the direct function and hyperbolic functions > Involving algebraic functions of cosh > Involving (a+b cosh(2c z))beta





http://functions.wolfram.com/01.22.21.0365.01









  


  










Input Form





Integrate[Sqrt[a + b Cosh[2 c z]] Coth[c z]^4, z] == ((-(-2 a^2 - 2 a b + 3 b^2 + 4 (a^2 + a b - b^2) Cosh[2 c z] + b (2 a + 3 b) Cosh[4 c z])) Coth[c z] Csch[c z]^2 - 2 I (7 a^2 + 16 a b + 9 b^2) Sqrt[(a + b Cosh[2 c z])/(a + b)] EllipticE[I c z, (2 b)/(a + b)] + 8 I (a^2 - b^2) Sqrt[(a + b Cosh[2 c z])/(a + b)] EllipticF[I c z, (2 b)/(a + b)])/ (6 (a + b) c Sqrt[a + b Cosh[2 c z]])










Standard Form





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MathML Form







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Rule Form





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





2002-12-18





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