We present the results of a search for neutrino point sources using the IceCube data collected between April 2008 and May 2011 with three partially completed configurations of the detector: the 40-, 59- and 79-string configurations. The live-time of this data set are 1,040 days. An unbinned maximum likelihood ratio test was used to search for an excess of neutrinos above the atmospheric background at any given direction in the sky. By adding two more years of data with improved event selection and reconstruction techniques, the sensitivity was improved by a factor 3.5 or more with respect to the previously published results obtained with the 40-string configuration of IceCube. We performed an all-sky survey and a dedicated search using a catalog of textit{a priori} selected objects observed by other telescopes. In both searches, the data are compatible with the background-only hypothesis. In the absence of evidence for a signal, we set upper limits on the flux of muon neutrinos. For an E$^{-2}$ neutrino spectrum, the observed limits are between 0.9 and $23.2times 10^{-12}$ TeV$^{-1}$ cm$^{-2}$s$^{-1}$. We also report upper limits for neutrino emission from groups of sources which were selected according to theoretical models or observational parameters and analysed with a stacking approach.
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