Transformation Properties of x'' + f₁ (t) x' + f2 (t) x + f3 (t) xⁿ = 0

The author studies the integrability of the nonlinear second-order ordinary differential equation described in the title. Using the invertible point transformation technique, Lie point symmetry technique and the Painlevé analysis, he classifies all integrable cases. The Lie algebra structure of the Lie point symmetries is also discussed. Finally, the three different methods are compared.