In this technical note, high dimensional integral Lyapunov functions are introduced for a class of MIMO nonlinear systems with unknown nonlinearities. First, adaptive state feedback control is presented based on the integral Lyapunov function. When only the output is measurable, by using a high-gain observer to estimate the derivative of the system output, adaptive output feedback control is also derived. The proposed control scheme provides a general approach to stabilize the MIMO plant without any restrictive assumptions. The control is continuous and ensures closed-loop stability and convergence of the tracking error to a small residual set. The size of the tracking error at steady state can be specified a priori and guaranteed by choosing the design parameters.