Accreting millisecond X-ray pulsars: 10 years of INTEGRAL observations

During the last 10 years, INTEGRAL made a unique contribution to the study of accreting millisecond X-ray pulsars (AMXPs), discovering three of the 14 sources now known of this class. Besides increasing the number of known AMXPs, INTEGRAL also carried out observations of these objects above 20 keV, substantially advancing our understanding of their behaviour. We present here a review of all the AMXPs observed with INTEGRAL and discuss the physical interpretation of their behaviour in the X-ray domain. We focus in particular on the lightcurve profile during outburst, as well as the timing, spectral, and thermonuclear type-I X-ray bursts properties.