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

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2002-12-18