On the criteria for integrability of the Liénard equation

Abstract: The Li\'{e}nard equation is of a high importance from both mathematical and physical points of view. However a question about integrability of this equation has not been completely answered yet. Here we provide a new criterion for integrability of the Li\'{e}nard equation using an approach based on nonlocal transformations. We also obtain some of previously known criteria for integrability of the Li\'{e}nard equation as a straightforward consequences of our approach's application. We illustrate our results by several new examples of integrable Li\'{e}nard equations.