In this paper, we investigate the ergodic capacity for distributed antenna systems over Rayleigh fadings, including a distance-dependent pathloss model. Based on the proof of asymptotic normality, the mean and the variance of the instantaneous capacity were recently presented as a closed form solution, which includes a root of polynomials. However, this solution is too complicated to capture quantitative performance measures such as multiplexing gain and power offset. In this work, we derive a simple and accurate expression for the ergodic capacity by utilizing the high signal-to-noise ratio (SNR) analysis. Our simple solution provides meaningful insights on how the ergodic capacity is affected as SNR, pathloss and antenna configurations change. Numerical results confirm the validity of our analytical results under a realistic pathloss model.