A simplified method of evaluating functionals of solutions of Fredholm integral equations using the b and h functions reported in RM-5295-PR. RM-5295-PR showed that all the important functions of multiple scattering could be expressed with ease in terms of the simpler b and h, which represent the internal specific intensities in atmospheres illuminated isotropically from the top (b) or bottom (h). A more generalized mathematical treatment is presented in this study. The functions b and h depend on only three variables, whereas I depends on four, and their use avoids a matrix inversion. 11 pp. Refs.