  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 ~ 0.1-0.2 mu G.
