The main object of this paper is to give sufficient conditions for the general integral operator , to be univalent in the open disk , when for all . This general integral operator was considered in a recent work [Bărbatu, C. and Breaz, D., Classes of an univalent integral operator, Studia Univ. Babe\c s-Bolyai Math., accepted]. The results derived in this paper are shown to follow upon specializing the parameters involved in our results. Several corollaries of the main results are also considered.