In this paper, we analyze the capacity of a Variable Spreading Gain Code Division Multiple Access (VSG-CDMA) system. Multi-rate data services will be supported in Wideband CDMA systems. VSG-CDMA is one way of implementing multi-rate systems, the other being multi-code CDMA. The intergration of voice, low, speed data and high speed data is considered in the analysis. We also consider various data rates with different QoS requirements and activity levels. The capacity estimate of this integrated system is the maximum number of concurrent voice users, low speed data users and high speed data users that the system can support while the required QoS and outage probability measures are met. We analytically find the admissible region of multiple services with data rates ranging from 8 kbps to 256 kbps in a wideband CDMA system with 5 MHz bandwidth.