  We compute $\epsilon$-factorized differential equations for all
dimensionally-regularized integrals of the nonplanar hexa-box topology, which
contribute for instance to 2-loop 5-point QCD amplitudes. A full set of pure
integrals is presented. For 5-point planar topologies, Gram determinants which
vanish in $4$ dimensions are used to build compact expressions for pure
integrals. Using unitarity cuts and computational algebraic geometry, we obtain
a compact IBP system which can be solved in 8 hours on a single CPU core,
overcoming a major bottleneck for deriving the differential equations.
Alternatively, assuming prior knowledge of the alphabet of the nonplanar
hexa-box, we reconstruct analytic differential equations from 30 numerical
phase-space points, making the computation almost trivial with current
techniques. We solve the differential equations to obtain the values of the
master integrals at the symbol level. Full results for the differential
equations and solutions are included as supplementary material.
