  We present the first comprehensive search for high-energy neutrino emission
from high- and low-mass X-ray binaries conducted by IceCube. Galactic X-ray
binaries are long-standing candidates for the source of Galactic hadronic
cosmic rays and neutrinos. The compact object in these systems can be the site
of cosmic-ray acceleration, and neutrinos can be produced by interactions of
cosmic rays with radiation or gas, in the jet of a microquasar, in the stellar
wind, or in the atmosphere of the companion star. We study X-ray binaries using
7.5 years of IceCube data with three separate analyses. In the first, we search
for periodic neutrino emission from 55 binaries in the Northern Sky with known
orbital periods. In the second, the X-ray light curves of 102 binaries across
the entire sky are used as templates to search for time-dependent neutrino
emission. Finally, we search for time-integrated emission of neutrinos for a
list of 4 notable binaries identified as microquasars. In the absence of a
significant excess, we place upper limits on the neutrino flux for each
hypothesis and compare our results with theoretical predictions for several
binaries. In addition, we evaluate the sensitivity of the next generation
neutrino telescope at the South Pole, IceCube-Gen2, and demonstrate its power
to identify potential neutrino emission from these binary sources in the
Galaxy.
