Continuous neutron slowing down theory, as generalized to incorporate inelastic scattering, has been combined with integral transport theory by use of the separable kernel analogy. The result is a matrix form of continuous slowing down theory where the matrices involved are direct generalizations of the scalar quantities encountered in continuous slowing down theory. The approach has been applied to the calculation of space-dependent spectra in uranium and iron single-region problems and in two-region problems involving uranium and iron. In general, very good agreement with more precise calculations is obtained.