This paper presents a derivation of an expression for the ergodic capacity of spatial multiplexing multiple-input-multiple-output (MIMO) systems with zero-forcing (ZF) receivers and independent substream detection. Assuming that the channel is unknown at the transmitter but known at the receiver, the ergodic capacity is formulated as a function of log-normal shadowing and Rayleigh fading. Gauss-Hermite quadrature integration is used to approximate the ergodic capacity expression in a concise form. The proposed analytical approach allows investigation of the effects of the shadowing standard deviation and the transmit correlation. Numerical and simulation results confirm that under various composite channel scenarios, the analytical results match well with the simulation results.