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.
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