The (3)He(d,p)(4)He reaction has been studied from E(c.m.)=600 keV down to astrophysical energies by means of the "Trojan horse" method using the (6)Li((3)He,p alpha)(4)He three-body reaction at E(lab)=5 and 6 MeV. Coincidence spectra were measured in kinematic conditions favoring the quasifree (3)He+(2)H process. The bare astrophysical factor S(b)(E) for the (3)He(d,p)(4)He reaction was extracted from the three-body cross section in the modified plane-wave Born approximation. Comparison with the S(b) extrapolation from the free two-body data is presented. The independent estimate of the screening potential as obtained with the present work seems to confirm the theoretical adiabatic limit.