[en] In this paper, the relativistic double differential cross sections for Compton scattering of photons from Cu, Sn, and Pb within the impulse approximation <2,3,5,7> have been theoretically calculated and compared with experiments. Two calculations have been performed for each atom, the first with the X-factor outside the integral and the second within the integral <5>. The latter calculation was carried out earlier by Reineking <10> with nearly the same results. For Cu and Sn the problem has also been solved with nonrelativistic initial wave functions. The purpose of this work has been to test the validity of the impulse approximation for different expressions of the Compton cross section with use of the calculations mentioned above. (author)