In this paper we develop a class of generalized extrapolation methods for numerical solution of nonlinear Fredholm integral equations of the second kind. The direct representation of this class allows us to simply discretize the nonlinear integral equations with smooth kernels. This approach enjoys several outstanding features of numerical methods such as: economized computational cost, the high order accuracy, direct implementation, discrretization on arbitrary nodes and applying the methods with positive weights. The comparison results demonstrate the superior results of the new class of methods versus the classical and recent approaches.