Systematization of Basic Divergent Integrals in Perturbation Theory and   Renormalization Group Functions
  We show that to n loop order the divergent content of a Feynman amplitude is spanned by a set of basic (logarithmically divergent) integrals which need not be evaluated. Only the coefficients of the basic divergent integrals are necessary to determine renormalization group functions. Relations between these coefficients of different loop orders are derived. 
L. C. T. Brito, H. G. Fargnoli, A. P. Ba\^eta Scarpelli, Marcos   Sampaio, M. C. Nemes