Recently, we proposed a new self-consistent integral equation to obtain the pair correlation function of simple fluids in the case of pairwise additive forces [J. Chem. Phys. 114, 4141 (2001)]. Here this integral equation is applied to predict the structural and thermodynamic properties of xenon at supercritical temperatures and low densities, with the aim of examining the possible effect of the three-body dispersion forces. The validity of our extended integral equation is tested against molecular dynamics, and the results are compared to recent small-angle neutron scattering measurements [Formisano et al. Phys. Rev. E 58, 2648 (1998)] and thermodynamic properties. The good agreement found between semianalytic calculations and simulation or experimental results of the structural and thermodynamic properties gives clear indication of the efficiency of the use of our integral equation conjugated with an effective pair potential consisting of the Aziz-Slaman two-body potential plus the Axilrod-Teller three-body potential.