  In this work, we compare the SFRs and SFHs of AGN and non-AGN galaxies. We
explore these aspects across different density fields and over three orders of
magnitude in L$_X$. For that purpose, we employ X-ray AGN detected in the
XMM-XXL field and construct a galaxy control sample, using sources from the
VIPERS catalogue. Our final samples consist of 149 X-ray AGN with $\rm
42<log,[L_{X,2-10keV}(ergs^{-1})]<45$ and 3\,488 non-AGN systems. The sources
span a redshift range of $\rm 0.5<z<1.0$ and $10.5<\rm
log\,[M_*(M_\odot)]<11.5$. For these systems, there are available measurements
for their local densities and their spectral lines from the VIPERS catalogue.
To compare the SFR of these two populations, we calculate the SFR$_{norm}$
parameter. The latter is defined as the ratio of the SFR of AGN to the SFR of
non-AGN galaxies with similar M$_*$ and redshift. Our findings reveal that low
and moderate L$_X$ AGN that live in low density fields have a nearly flat
SFR$_{norm}-$L$_X$ relation. In contrast, AGN of similar L$_X$ that live in
high density environments present an increase of SFR$_{norm}$ with L$_X$.
Notably, our results suggest that the most luminous of the AGN exhibit
increased SFR relative to non-AGN galaxies, and this trend appears to be
independent of the density of the environment. Furthermore, for AGN with
similar L$_X$, those in high-density regions tend to have higher SFR$_{norm}$
values compared to their counterparts in low-density areas. Comparison of the
D$_n$4000 spectral index, which serves as a proxy for the age of the stellar
population, reveals that low-to-moderate L$_X$ AGN live in galaxies with
comparable stellar populations with non-AGN systems, regardless of the density
field they live in. However, the most luminous X-ray sources tend to live in
galaxies that have younger stellar populations than non-AGN galaxies,
regardless of the galaxy's environment.
