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In the numerical integration of an improper integral of the first kind, it is customary to truncate the integral when the change yielded by the last iteration is less than some predetermined constant. The efficiency of such integration schemes can often be improved by use of recent advances in the theory of nonlinear transformations; however, for several important integrals, e.g. integrals whose integrands are rational polynomials these transformations fail to yield much improvement. In this paper, several methods of convergence improvement are developed which greatly improve convergence of some improper integrals, including the integrals of rational polynomials. [ABSTRACT FROM AUTHOR]