Artificial intelligence (AI) is rapidly being integrated into university curricula, yet quantitative indicators of AI use reveal little about how learners use AI as a learning resource or what educational outcomes follow. This cross-sectional study of 212 university students enrolled in AI-integrated courses examined the associations of AI literacy, instructor feedback, the proportion of in-class AI use, and total weekly AI use time with self-perceived cognitive learning outcomes, measured across the six cognitive processes of the revised Bloom's taxonomy (remember, understand, apply, analyze, evaluate, and create). Confirmatory factor analyses supported largely acceptable multidimensional and higher-order structures for self-perceived cognitive learning outcomes and AI literacy, although discriminant validity between some factors was limited. A regression model with the four predictors explained 46.3% of the variance in overall self-perceived cognitive learning outcomes (R²=.463). When all predictors were considered simultaneously, only AI literacy showed a significant positive association (B=.615, 95% CI [.475, .754], p< .001); instructor feedback and the two AI use indicators did not. AI literacy remained significantly associated with all six cognitive domains after Benjamini–Hochberg correction. These findings suggest that universities should distinguish the quantity of AI use from learners' capacity to understand, evaluate, and self-regulate their use of AI.