Large language models (LLMs) have notably progressed in multi-step and long-chain reasoning. However, extending their reasoning capabilities to encompass deep interactions with search remains a non-trivial challenge, as models often fail to identify optimal reasoning–search interaction trajectories, resulting in suboptimal responses. We propose R-Search, a novel reinforcement learning framework for Reasoning–Search integration, designed to enable LLMs to autonomously execute multi-step reasoning with deep search interaction, and learn optimal reasoning–search interaction trajectories via multi-reward signals, improving response quality in complex logic- and knowledge-intensive tasks. R-Search guides the LLM to dynamically decide when to search or reason, while globally integrating key evidence to enhance deep knowledge interaction between reasoning and search. During RL training, R-Search provides multi-type rewards to jointly optimize the reasoning–search trajectory. Experiments on seven datasets show that R-Search significantly outperforms mainstream RAG baselines.