Abstract: An introduction to a recently established lemma is presented. The lemma enables us to evaluate integrals involving powers and exponentials on a large semicircle. Based on the lemma and the residue theorem, two general for- mulae are derived for infinite integrals are expressed in terms of residues and involving powers, rational functions and trigonometric functions, and the results Laurent coefficients of the rational function. Several examples are given.

Key words: infinite integrals, residue theorem, powers, rational functions, trigonometric functions