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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 algebraic functions of the direct function and hyperbolic functions > Involving sinh > Involving sinh(c z)(a+b coth2(c z))beta





http://functions.wolfram.com/01.22.21.0399.01









  


  










Input Form





Integrate[Sinh[c z] Sqrt[a + b Coth[c z]^2], z] == (I Sqrt[2] Sqrt[1/a] b Cosh[c z] Sqrt[a + b Coth[c z]^2] (EllipticE[I ArcSinh[(Sqrt[1/a] Sqrt[-a + b + (a + b) Cosh[2 c z]])/ Sqrt[2]], -(a/b)] - EllipticF[ I ArcSinh[(Sqrt[1/a] Sqrt[-a + b + (a + b) Cosh[2 c z]])/Sqrt[2]], -(a/b)]) Sqrt[-(((a + b) Sinh[c z]^2)/b)])/ (c Sqrt[((a + b) Cosh[c z]^2)/a] Sqrt[-a + b + (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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