A new method for solving the integral equation based on the Omstein-Zernike equation for binary mixture is proposed. Then the radial distribution function obtained for both the Percus-Yevick and the hypernetted chain closure equations are used to calculate the residual chemical potential at infinite-dilution and at reduced temperatures T* = 2, 1.5 (supercritical isotherms) over a varying range of reduced densities rho* = 0.1 to 0.6 for various types of the Lennard-jones mixture in terms of size ratios D and energy ratios C. To examine the ability of the integral equation approach for the residual chemical potential calculations, the results are compared with the Monte-Carlo simulation data and the van der Waals I results (Shing et al., 1988). It is seen that at rho* = 0.1 to 0.5, the deviation of the integral equation results from the MC simulation data is less than the reported statistical fluctuation.