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We consider Feynman integrals with algebraic leading singularities and totaldifferentials in $\epsilon\,\mathrm{d}\ln$ form. We show for the first timethat it is possible to evaluate integrals with singularities involvingunrationalizable roots in terms of conventional multiple polylogarithms, byeither parametric integration or matching the symbol. As our main application,we evaluate the two-loop master integrals relevant to the $\alpha \alpha_s$corrections to Drell-Yan lepton pair production at hadron colliders. Weoptimize our functional basis to allow for fast and stable numericalevaluations in the physical region of phase space.

Multiple polylogarithms with algebraic arguments and the two-loop EW-QCD Drell-Yan master integrals