Using exponential generating functions to evaluate definite integrals

Numerous examples where various types of de nite integrals evaluated using a technique exploiting exponential generating functions are presented. We show how some classically famous but tricky integrals can be readily found using such an approach. Brief historical remarks on some of the more notable integrals considered are made. Application of some of the integrals found to a class of classically important series containing the central binomial coefficients are given.