We present the results of deep observations of the Ophiuchus cluster of galaxies with INTEGRAL in the 3-80 keV band .
We analyse 3 Ms of INTEGRAL data on the Ophiuchus cluster with the IBIS/ISGRI hard X-ray imager and the JEM-X X-ray monitor .
In the X-ray band using JEM-X , we show that the source is extended , and that the morphology is compatible with the results found by previous missions .
Above 20 keV , we show that the size of the source is slightly larger than the PSF of the instrument , and is consistent with the soft X-ray morphology found with JEM-X and ASCA .
Thanks to the constraints on the temperature provided by JEM-X , we show that the spectrum of the cluster is not well fitted by a single-temperature thermal Bremsstrahlung model , and that another spectral component is needed to explain the high energy data .
We detect the high energy tail with a higher detection significance ( 6.4 \sigma ) than the BeppoSAX claim ( 2 \sigma ) .
Because of the imaging capabilities of JEM-X and ISGRI , we are able to exclude the possibility that the excess emission comes from very hot regions or absorbed AGN , which proves that the excess emission is indeed of non-thermal origin .
Using the available radio data together with the non-thermal hard X-ray flux , we estimate a magnetic field B \sim 0.1 - 0.2 \mu G .