  We present analytic results for all the Feynman integrals relevant for
${\mathcal O}(\alpha \alpha_s)$ virtual corrections to $H \rightarrow ZZ^*$
decay. We use the method of differential equations to solve the master
integrals while keeping the full dependence on the masses of all the particles
including internal propagators. Due to the presence of four mass scales we
encounter multiple square roots. We argue that all the occurring square roots
can not be rationalized at the same time as a simultaneous rationalization
brings us to integrals over $CY_3$ manifolds. Hence we rationalize only three
square roots simultaneously and construct suitable ans\"atze to obtain
dlog-forms containing the square root, after obtaining an epsilon-factorised
form for the differential equations. We present the alphabet and the analytic
form of all the boundary constants that appear in the solutions of the
differential equations. The results for master integrals are expressed in terms
of Chen's iterated integrals with dlog one-forms.
