The accuracy of both hypernetted chain (HNC) and Kovalenko-Hirata (KH) approximations assumed in an Ornstein-Zernike integral equation theory has been studied in terms of the solvation free energy (SFE) by comparing with molecular dynamics simulation for Lennard-Jones liquid. The Lennard-Jones parameters for the solute, epsilon(u) and sigma(u), were systematically varied. epsilon(u)-dependence of the relative SFE is found to be hardly dependent on the approximations. However, sigma(u)-dependences of the SFE obtained both from HNC and KH approximations considerably differ from those by molecular dynamics simulation. The source of the error in the SFE from both approximations is also discussed. (C) 2014 Elsevier B.V. All rights reserved.