The author presents a method for the approximate solution of the Fredholm integral equation \[ \int^b_a u(t)L(t, t_0)dt= v(t_0),\quad a\leq t_0\leq b, \] with kernel \[ L(t, t_0)= \ln\Biggl({1\over d(t, t_0)}\Biggr),\quad d(t, t_0)= \sqrt{(x(t)- x(t_0))^2- (y(t)- y(t_0))^2}. \] The main idea is to consider the unknown function \(u(t)\) as product of two functions, one of which is singular such that its singularities can be isolated via change of variables and the second one is expanded in a Taylor series with unknown coefficients. Adequate numerical examples are presented.