In this Letter, we propose a comprehensive framework for performance analysis of cooperative wireless systems using Amplify and Forward (AF) relay methods. The framework relies on the Moment Generating Function (MGF-) based approach for performance analysis of communication systems over fading channels, and on some properties of the Laplace Transform, which allow to develop a single-integral relation between the MGF of a random variable and the MGF of its inverse. Moreover, a simple lower bound for Outage Probability (Pout) and Outage Capacity (OC) computation is also introduced. Numerical and simulation results are provided to substantiate the accuracy of the proposed framework.