In the framework solving electromagnetic scattering problems with a Leontovich impedance boundary condition (LIBC), the numerical resolution requires the evaluation of singular integrals appearing in the discretization of the variational formulation. Our main interest is to pricisely evaluate these integrals. Thus, we propose an analytic method to approximate it. The performance of this method will be evaluated by calculating the radar cross section (RCS). Then, we compare RCS to the Mie series solution for the unit sphere in various configurations.