  The standard way of evaluating residues and some real integrals through the
residue theorem (Cauchy's theorem) is well-known and widely applied in many
branches of Physics. Herein we present an alternative technique based on the
negative dimensional integration method (NDIM) originally developed to handle
Feynman integrals. The advantage of this new technique is that we need only to
apply Gaussian integration and solve systems of linear algebraic equations,
with no need to determine the poles themselves or their residues, as well as
obtaining a whole class of results for differing orders of poles
simultaneously.
