Weighted model integration (WMI) extends weighted model counting to integration in mixed discrete-continuous domains. It has shown tremendous promise for solving probabilistic inference problems in graphical models and probabilistic programs. Yet, state-of-the-art tools for WMI have limited performance and ignore the independence structure that is crucial to improving efficiency. To address this limitation, we propose an efficient model integration algorithm for theories with tree pri-mal graphs. We exploit the sparse graph structure by using search to performing integration. Our algorithm greatly improves the computational efficiency on such problems and exploits context-specific independence between variables. Experimental results show dramatic speedups compared to existing WMI solvers on problems with tree-shaped dependencies.