  We hereby derive the Newtonian metric potentials for the fourth-derivative
gravity including the one-loop logarithm quantum corrections. It is explicitly
shown that the behavior of the modified Newtonian potential near the origin is
improved respect to the classical one, but this is not enough to remove the
curvature singularity in $r=0$. Our result is grounded on a rigorous proof
based on numerical and analytic computations.
