Integrate[Sqrt[(a + b Cot[c z]^2)^3], z] == (1/c) (Sqrt[(a + b Cot[c z]^2)^3] Sin[c z] (-((b Cos[c z])/(a + b + (-a + b) Cos[2 c z])) - (I (1 + Cos[c z]) Sqrt[-((a + b + (-a + b) Cos[2 c z])/(1 + Cos[c z])^2)] ((3 a - 2 b) Sqrt[b] Sqrt[-a + b] Log[(1/Sqrt[b]) (-8 I a + 4 I b + 2 Cot[(c z)/2]^2 (-2 I b + Sqrt[2] Sqrt[b] Sqrt[(-a - b + (a - b) Cos[2 c z]) Sec[(c z)/2]^4]))] + 4 (a - b)^2 Log[-((1/(4 Sqrt[-a + b])) (Cos[(c z)/2]^2 (2 I a - 2 I b + Sqrt[2] Sqrt[-a + b] Sqrt[(-a - b + (a - b) Cos[2 c z]) Sec[(c z)/2]^4] - 2 I (a - b) Tan[(c z)/2]^2)))] + Sqrt[b] Sqrt[-a + b] (-3 a + 2 b) Log[Sqrt[2] Sqrt[(-a - b + (a - b) Cos[2 c z]) Sec[(c z)/2]^4] - (2 I (2 a - b + b Tan[(c z)/2]^2))/Sqrt[b]]) Sin[c z]^2)/ (Sqrt[2] Sqrt[-a + b] (a + b + (-a + b) Cos[2 c z])^2)))

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2002-12-18