Measuring the spin up of the accreting millisecond pulsar XTE J1751-305

We perform a timing analysis on RXTE data of the accreting millisecond pulsar XTE J1751- 305 observed during the 2002 April outburst. After having corrected for Doppler effects on the pulse phases due to the orbital motion of the source, we performed a timing analysis on the phase delays, which gives, for the first time for this source, an estimate of the average spin frequency derivative <nu > = (3.7 +/- 1.0) x 10(-13) Hz s(-1). We discuss the torque resulting from the spin-up of the neutron star deriving a dynamical estimate of the mass accretion rate and comparing it with the one obtained from X-ray flux. Constraints on the distance to the source are discussed, leading to a lower limit of similar to 6.7 kpc.