A new iterative method for numerical integration of rational functions on the
real line is presented. The algorithm transforms the rational integrand into a new rational function preserving the integral on the line. The
coefficients of the new function are explicit polynomials in the original ones.
These transformations depend on the degree of the input and the desired order
of the method. Both parameters are arbitrary. The formulas can be precom-
puted. Iteration yields an approximation of the desired integral with m-th
order convergence. Examples illustrating the automatic generation of these
formulas and the numerical behaviour of this method are given.
