  In this paper, we describe a general method for computing Selberg-like
integrals based on a formula, due to Kaneko, for Selberg-Jack integrals. The
general principle consists in expanding the integrand \emph{w.r.t.} the Jack
basis, which is obtained by a Gram-Schmidt orthogonalization process.
  The resulting algorithm is not very efficient because of this decomposition.
But for special cases, the coefficients admit a closed form. As an example, we
study the case of the power-sums since for which the coefficients are obtained
by manipulating generating series by means of transformations of alphabets.
Furthermore, we prove that the integral is a rational function in the number of
variables which allows us to study asymptotics. As an application, we
investigate the asymptotic behavior when the integrand involves Jack
polynomials and power sums.
