Context : Aims : The synthesis of the cosmic X-ray background ( CXB ) requires a large population of Compton-thick active galactic nuclei that have not been detected so far . We probe whether bright infrared galaxies could harbor a population of Compton-thick nuclei and if they could contribute significantly . Methods : We analyzed 112 Msec of INTEGRAL Â observations obtained on 613 galaxies from the IRAS Revised Bright Galaxy Sample . We derived the average hard X-ray ( 18-80 keV ) emission of Seyfert and various non Seyfert galaxy subsamples to estimate their relative contribution to the locally emitted CXB . Results : The Seyfert 1 & 2 are detected at hard X-rays . None of the other galaxy subsamples were detected . ULIRGs are at least 5 times under-luminous at hard X-rays when compared to Seyferts . The upper limit obtained for the average non Seyfert galaxies is as low as 7 \times 10 ^ { -13 } erg s ^ { -1 } cm ^ { -2 } . On average , these galaxies do not contain active nuclei brighter than 10 ^ { 41 } ~ { } { erg / s } at hard X-rays . The total hard X-ray flux detected from the sample is 4.9 \times 10 ^ { -9 } erg s ^ { -1 } cm ^ { -2 } ( about 1 % of the CXB ) , and 64 % of this originates in absorbed active nuclei . Local non-Seyfert galaxies contribute for less than 7 % and do not harbor the Compton-thick nuclei assumed to synthesize the locally emitted CXB . Conclusions :