The IceCube detector took data in its 22-string configuration in 2007-2008. This data has been analyzed to search for extraterrestrial point sources of neutrinos using several methods. Two main methods are discussed and compared here: the binned and the unbinned maximum likelihood method. The best sky-averaged sensitivity (90% C.L.) is E^2 Phi_nu_mu=1.3 10^-11 TeVcm^-2s^-1 to a generic E^-2 flux of nu_mu over the energy range from 3 TeV to 3 PeV. No neutrino point sources are found from the individual directions of a pre-selected catalogue nor in a search extended to the northern sky. Limits are improved by a factor of two compared to the total statistics collected with the AMANDA-II detector and represent the best results to date.

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