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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 and tanh





http://functions.wolfram.com/01.22.21.0413.01









  


  










Input Form





Integrate[(d Coth[c z]^2 + e Sinh[c z])/Sqrt[(a + b Tanh[c z]^2)^3], z] == (Sech[c z] (d Coth[c z]^2 + e Sinh[c z]) (-((1/a^2) ((a + b) (a - b + (a + b) Cosh[2 c z]) Csch[c z] 1 ((a^3 + a^2 b - 2 a b^2 - 2 b^3) d + (a^3 + 3 a^2 b + 4 a b^2 + 2 b^3) d Cosh[2 c z] + 2 a^2 b e Sinh[c z]))) + (a - b + (a + b) Cosh[2 c z])^(3/2) ((2 (a + b) e Sqrt[a - b + (a + b) Cosh[2 c z]] Sqrt[(a - b + (a + b) Cosh[2 c z])/(1 + Cosh[c z])^2])/ Sqrt[(a - b + (a + b) Cosh[2 c z]) Sech[(c z)/2]^4] + Sqrt[2] d Csch[c z]^3 Log[Sqrt[a - b + (a + b) Cosh[2 c z]] + Sqrt[2] Sqrt[(a + b) Sinh[c z]^2]] ((a + b) Sinh[c z]^2)^(3/2))) Tanh[c z]^2)/((a + b)^3 c (2 d + 2 d Cosh[2 c z] - 3 e Sinh[c z] + e Sinh[3 c z]) Sqrt[(a + b Tanh[c z]^2)^3])










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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