  We present the 0.5 - 78 keV spectral analysis of 18 broad line AGN belonging
to the INTEGRAL complete sample. Using simultaneous Swift-XRT and NuSTAR
observations and employing a simple phenomenological model to fit the data, we
measure with a good constraint the high energy cut-off in 13 sources, while we
place lower limits on 5 objects. We found a mean high-energy cut-off of 111 keV
(standard deviation = 45 keV) for the whole sample, in perfect agreement with
what found in our previous work using non simultaneous observations and with
what recently published using NuSTAR data. This work suggests that simultaneity
of the observations in the soft and hard X-ray band is important but not always
essential, especially if flux and spectral variability are properly accounted
for. A lesser agreement is found when we compare our cut-off measurements with
the ones obtained by Ricci et al. (2017) using Swift-BAT high energy data,
finding that their values are systematically higher than ours. We have
investigated whether a linear correlation exists between photon index and the
cut-off and found a weak one, probably to be ascribed to the non perfect
modelling of the soft part of the spectra, due to the poor statistical quality
of the 2-10 keV X-ray data. No correlation is also found between the Eddington
ratio and the cut-off, suggesting that only using high statistical quality
broad-band spectra is it possible to verify the theoretical predictions and
study the physical characteristics of the hot corona and its geometry.
