This paper is part of the collection initiated in [49], aiming to evaluate the entries in [35] and to provide some context. This table contains a large variety of entries involving the Bessel functions. The goal of the current work is to evaluate some entries in [35] where the integrand is an elementary function and the result involves the so-called modified Bessel function of the second kind, denoted by Kν(x). Other types of integrals containing Bessel functions will appear in a future publication. This introduction contains a brief description of the Bessel functions. The reader is referred to [16, 65, 67, 68] for more information about this class of functions.