[en] We have obtained, in a closed form, the energy levels of a one-dimensional anharmonic oscillator (a.o.) ax²+βx⁴ using the 1st order of the so-called modified perturbation theory (MPT) as well as WKB method. The calculations were performed for a broad range of the anharmonic constant β and energies. We prove that inaccuracy of the 1st order MPT for positive harmonic constant is not worse than 1-2%. We note that MPT final expressions are much simpler. Contrary to the WKB method there is no need in the preliminary solution of the transendental equation. A particularly simple formula is obtained for the energy levels of the pure quartic oscillator. It is found that for a < 0 and negative energies MPT is not satisfactory. On the other hand WKB method reasonably describes the energy levels and their splitting at the bottom of the potential well. We conclude that these methods complement each other