  We describe an efficient method for extracting the parts of $D$-dimensional
loop integrals that are needed to derive observables in classical general
relativity from scattering amplitudes. Our approach simplifies the soft-region
method of integration by judiciously combining terms before the final
integrations. We demonstrate the method by computing the required integrals for
black-hole scattering to the second Post-Minkowskian order in Einstein gravity
coupled to scalars. We also confirm recent results at the third
Post-Minkowskian order regarding universality and high-energy behavior of
gravitational interactions in maximal supergravity.
