  The paper presents the timing and spectral analysis of several observations
of the Crab pulsar performed with INTEGRAL in the energy range 3-500 keV. All
these observations, when summed together provide a high statistics data set
which can be used for accurate phase resolved spectroscopy. A detailed study of
the pulsed emission at different phase intervals is performed. The spectral
distribution changes with phase showing a characteristic reverse S shape of the
photon index. Moreover the spectrum softens with energy, in each phase
interval, and this behavior is adequately modeled over the whole energy range
3-500 keV with a single curved law with a slope variable with Log(E),
confirming the BeppoSAX results on the curvature of the pulsed emission. The
bending parameter of the log-parabolic model is compatible with a single value
of 0.14+/-0.02 over all phase intervals. Results are discussed within the
three-dimensional outer gap model.
