  We present the most complete study to date of the X-ray emission from
star-formation in high redshift (median z=0.7; z<1.5), IR-luminous
(L_IR=10^10-10^13 L_sun) galaxies detected by Herschel's PACS and SPIRE
instruments. For our purpose we take advantage of the deepest X-ray data to
date, the Chandra deep fields (North and South). Sources which host AGN are
removed from our analysis by means of multiple AGN indicators. We find an AGN
fraction of 18+/-2 per cent amongst our sample and note that AGN entirely
dominate at values of log[L_X/L_IR]>-3 in both hard and soft X-ray bands. From
the sources which are star-formation dominated, only a small fraction are
individually X-ray detected and for the bulk of the sample we calculate average
X-ray luminosities through stacking. We find an average soft X-ray to infrared
ratio of log[L_SX/L_IR]=-4.3 and an average hard X-ray to infrared ratio of
log[L_HX/L_IR]=-3.8. We report that the X-ray/IR correlation is approximately
linear through the entire range of L_IR and z probed and, although broadly
consistent with the local (z<0.1) one, it does display some discrepancies. We
suggest that these discrepancies are unlikely to be physical, i.e. due to an
intrinsic change in the X-ray properties of star-forming galaxies with cosmic
time, as there is no significant evidence for evolution of the L_X/L_IR ratio
with redshift. Instead they are possibly due to selection effects and remaining
AGN contamination. We also examine whether dust obscuration in the galaxy plays
a role in attenuating X-rays from star-formation, by investigating changes in
the L_X/L_IR ratio as a function of the average dust temperature. We conclude
that X-rays do not suffer any measurable attenuation in the host galaxy.
