  This paper deals with a general class of integrals, the particular cases of
which are connected to outstanding problems in astronomy and physics. Reaction
rate probability integrals in the theory of nuclear reaction rates, Kr\"atzel
integrals in applied analysis, inverse Gaussian distribution, generalized
type-1, type-2 and gamma families of distributions in statistical distribution
theory, Tsallis statistics and Beck-Cohen superstatistics in statistical
mechanics and the general pathway model are all shown to be connected to the
integral under consideration. Representations of the integral in terms of
generalized special functions such as Meijer's G-function and Fox's H-function
are also pointed out.
