  We evaluate a four-loop conformal integral, i.e. an integral over four
four-dimensional coordinates, by turning to its dimensionally regularized
version and applying differential equations for the set of the corresponding
213 master integrals. To solve these linear differential equations we follow
the strategy suggested by Henn and switch to a uniformly transcendental basis
of master integrals. We find a solution to these equations up to weight eight
in terms of multiple polylogarithms. Further, we present an analytical result
for the given four-loop conformal integral considered in four-dimensional
space-time in terms of single-valued harmonic polylogarithms. As a by-product,
we obtain analytical results for all the other 212 master integrals within
dimensional regularization, i.e. considered in D dimensions.
