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.
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