With the development of Ethereum, numerous blockchains compatible with Ethereum's execution environment (i.e., Ethereum Virtual Machine, EVM) have emerged. Developers can leverage smart contracts to run various complex decentralized applications on top of blockchains. However, the increasing number of EVM-compatible blockchains has introduced significant challenges in cross-chain interoperability, particularly in ensuring efficiency and atomicity for the whole cross-chain application. Existing solutions are either limited in guaranteeing overall atomicity for the cross-chain application, or inefficient due to the need for multiple rounds of cross-chain smart contract execution. To address this gap, we propose IntegrateX, an efficient cross-chain interoperability system that ensures the overall atomicity of cross-chain smart contract invocations. The core idea is to deploy the logic required for cross-chain execution onto a single blockchain, where it can be executed in an integrated manner. This allows cross-chain applications to perform all cross-chain logic efficiently within the same blockchain. IntegrateX consists of a cross-chain smart contract deployment protocol and a cross-chain smart contract integrated execution protocol. The former achieves efficient and secure cross-chain deployment by decoupling smart contract logic from state, and employing an off-chain cross-chain deployment mechanism combined with on-chain cross-chain verification. The latter ensures atomicity of cross-chain invocations through a 2PC-based mechanism, and enhances performance through transaction aggregation and fine-grained state lock. We implement a prototype of IntegrateX. Extensive experiments demonstrate that it reduces up to 61.2% latency compared to the state-of-the-art baseline while maintaining low gas consumption.