Unlike the Recursive Risch Algorithm for the integration of transcendental elementary functions, the Risch-Noiman Method processes the tower of field extensions directly in one step. In addition to logarithmic and exponential field extensions, this method can handle extensions in terms of tangents. Consequently, it allows trigonometric functions to be treated without converting them to complex exponential form. We review this method and describe its implementation in MAPLE. A heuristic enhancement to this method is also presented.