Rectifying Transformations for the Integration of Rational Trigonometric Functions

The paper present four rectifying transformations that can be applied to the integration of a real rational expression of trigonometric functions. Integration is with respect to a real variable. The transformations remove, from the real line, discontinuities and singularities that would otherwise appear. If the integration is with respect to a complex variable, the transformations remain valid. In that case, they move singularities from the real line to elsewhere in the complex plane.