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An integrated cellular and short-range network, in which short-range communications among users are used as a mean of increasing the performance of a cellular system, is considered as a promising technology to support various multimedia services in an efficient manner. Especially for multicast service, this kind of network can provide a method to overcome a drawback of a conventional multicast, which is caused by applying a common data rate to multicast traffic. So, we study a cooperative multicast that utilizes the capability of the shortrange communications. In this case, the power consumption of a mobile device is unavoidable. Thus, we develop an optimization problem that finds the optimal data rates assigned to each user in a multicast group to minimize the power consumption of a mobile device. Simulation results show that the cooperative multicast based on the proposed rate control algorithm can reduce a large amount of transmit power of a base station while using a small amount of power of a mobile device.