  In this work we solved the equation of scalar and tensor perturbations for
the generalized Starobinsky inflationary model using the improved uniform
approximation method and the phase-integral method up to third-order in
deviation. We compare our results with the numerical integration. We have
obtained that both semiclassical methods reproduce the scalar power spectra
$P_{S,T}$, the scalar spectral index $n_S$, and the tensor-to-scalar ratio $r$.
Also we present our results in the $(n_S,r)$ plane.
