  We present the analytic calculation of the planar master integrals which
contribute to compute the two-loop light-fermion electroweak corrections to the
production of a Higgs boson in association with a jet in gluon-gluon fusion.
The complete dependence on the electroweak-boson mass is retained. The master
integrals are evaluated by means of the differential equations method and the
analytic results are expressed in terms of multiple polylogarithms up to weight
four.
