Recent works on the analysis of linear multiuser receivers for DS-CDMA applications have led to capacity-relevant expressions that are the solution of an integral equation involving Stieltjes transforms of the distribution of transmit powers. The key tools employed in these works are new results on the asymptotic eigenvalue distributions of random matrices. Unfortunately, it is only in the particular case of the transmit powers being equal that the integral equation has a closed form solution. This paper addresses the same problems pioneered in the afore-mentioned works, but demonstrates how an alternative solution is available that, while appealing to simpler mathematical ideas (principally, the law of large numbers), also offers flexibility in that the results obtained apply for arbitrary (as opposed to strictly constant) received powers. An additional advantage is that the convergence rate of the approximation used here can also be quantified.