Two observation campaigns performed in 2003 and 2004 with the INTEGRAL satellite have provided the first sensitive survey of the Large Magellanic Cloud with an imaging instrument in the hard X-ray range ( 15 keV - 10 MeV ) . The high energy flux and long term variability of the black hole candidate LMC X–1 was measured for the first time without the contamination of the nearby ( \sim 25 ^ { \prime } ) young pulsar PSR B0540–69 . We studied the accreting pulsar LMC X–4 , constraining the size of the hard X-ray emitting region ( \leq 3 \times 10 ^ { 10 } cm ) from the analysis of its eclipses , and measuring its spin period ( 13.497 \pm 0.005 s ) in the 20-40 keV band . LMC X–3 was not detected , being in a soft state during the first observation and possibly in an extremely low state in the second one . Thanks to the large field of view of the IBIS instrument , we could study also other sources falling serendipitously in the observed sky region around the LMC : the Galactic low mass X-ray binary EXO 0748–676 , the accreting pulsar SMC X-1 in the Small Magellanic Cloud , and the Active Galactic Nucleus IRAS 04575–7537 . In addition we discovered five new hard X-ray sources , two of which most likely belong to the LMC .