We show that the cohomology of the Becchi-Rouet-Stora diffeomorphism operator on the integrated functions in ${\mathrm{R}}^{d}$ can be easily computed as a series whose terms contain the cohomology elements of the same operator on the unintegrated functions. Then we find that this last cohomology space can be specified, in each sector classified according to its undifferentiated-ghosts content, by means of descent and antidescent equations, which can be studied with the aid of the spectral-sequences method. The general solutions, in arbitrary space-time dimensions, are provided in a very simple way, and the usual charge-one gravitational anomalies are recovered as the highest undifferentiated-ghost component of the unintegrated anomaly with Faddeev-Popov charge equal to d+1.