We have calculated excess chemical potentials of additive molecules in a bisphenol A-polycarbonate matrix using fast-growth thermodynamic integration. It is shown that this method, which is based on Jarzynski's nonequilibrium work theorem, is ideally suited to overcome some of the typical sampling problems one meets when inserting large additive molecules into a dense polymer matrix. The method provides a direct link between the calculated excess chemical potential and the atomic-scale environment preferred by the inserted molecule. We discuss for which types of free-energy landscapes fast-growth thermodynamic integration is well suited and which are the optimal parameters to use.