


IntegrationIntegration by Trigonometric Substitution 2We assume that you are familiar with the material in integration by trigonometric substitution 1 and geometric representation of trigonometric functions. Various methods are available for evaluating the integrals of rational functions (ratios of two polynomials). It has been discovered that a fractional expression involving trig functions can always be transformed into a rational function. Let u = tan . We can represent this in the following diagram: We deduce and . Hence,
Since all other trig functions can be written in terms of sin x and cos x all fractional expressions of trig functions can always be transformed into a rational function. ExampleConsider . Let u = tan then and . The integral simplifies to :
ExerciseTry all 5 of these. << Integration by Trigonometric Substitution I  Integration Index  