  We outline the computational details to obtain mixed EW-QCD corrections to
on-shell production of a single vector boson at the LHC at two-loop level. We
use the method of differential equation to obtain the pure virtual,
real-virtual and double-real master integrals. Finally, we obtain the ${\cal
O}(\alpha \alpha_s)$ corrections to the total partonic cross section of the
process $q \bar{q} \rightarrow Z + X$.
