  The three-loop master integrals for ladder-box diagrams with one massive leg
are computed from an eighty-five by eighty-five system of differential
equations, solved by means of Magnus exponential. The results of the considered
box-type integrals, as well as of the tower of vertex- and bubble-type master
integrals associated to subtopologies, are given as a Taylor series expansion
in the dimensional regulator parameter epsilon = (4-d)/2. The coefficients of
the series are expressed in terms of uniform weight combinations of multiple
polylogarithms and transcendental constants up to weight six. The considered
integrals enter the next-to-next-to-next-to-leading order virtual corrections
to scattering processes like the three-jet production mediated by vector boson
decay, V* -> jjj, as well as the Higgs plus one-jet production in gluon fusion,
pp -> Hj.
