Abstract : In the course of continuing investigations on the propagation of electromagnetic pulses, it became necessary to evaluate an integral involving exponential and Bessel functions. It was found that this integral had been evaluated incorrectly in the literature, and the error has been perpetuated for nearly 30 years. This memorandum evaluates the integral correctly, and shows that although the incorrect result had been expressed entirely in terms of algebraic and logarithmic functions, the correct result is considerably more complicated, and involves incomplete gamma functions. (Author)