  We study master integrals needed to compute the Higgs boson production cross
section via gluon fusion in the infinite top quark mass limit, using a
canonical form of differential equations for master integrals, recently
identified by Henn, which makes their solution possible in a straightforward
algebraic way. We apply the known criteria to derive such a suitable basis for
all the phase space master integrals in afore mentioned process at
next-to-next-to-leading order in QCD and demonstrate that the method is
applicable to next-to-next-to-next-to-leading order as well by solving a
non-planar topology. Furthermore, we discuss in great detail how to find an
adequate basis using practical examples. Special emphasis is devoted to master
integrals which are coupled by their differential equations.
