  The phase-integral approximation devised by Fr\"oman and Fr\"oman, is used
for computing cosmological perturbations in the quartic chaotic inflationary
model. The phase-integral formulas for the scalar power spectrum are explicitly
obtained up to fifth order of the phase-integral approximation. As in previous
reports [1-3], we point out that the accuracy of the phase-integral
approximation compares favorably with the numerical results and those obtained
using the slow-roll and uniform approximation methods.
