We develop and describe a general method for evaluating collision integrals in the linearized Boltzmann transport equation which eliminates the necessity to repeat similar integration steps for each force law. Integrations not dependent on scattering cross-section variables have been carried out once and for all. The two mathematical innovations which facilitate these general integrations are (i) the development of an expansion of the Burnett functionX NML(x+y) into products of Burnett functions of argument x with other functions; and (ii) the use of representations of the full rotation group to transform from space-fixed axes to axes aligned with the relative velocity vector of colliding atoms. The relations so derived allow rapid evaluation of the collision integral from a knowledge of the scattering cross section.