  A method, recently devised to obtain analytical approximations to certain
classes of integrals, is used in combination with the WKB expansion to derive
accurate analytical expressions for the spectrum of quantum potentials. The
accuracy of our results is verified by comparing them both with the literature
on the subject and with the numerical results obtained with a Fortran code. As
an application of the method that we propose, we consider the meson
spectroscopy with various phenomenological potentials.
