Integration using Euler's formula

In integral calculus, complex numbers and Euler's formula may be used to evaluate integrals involving trigonometric functions. Using Euler's formula, any trigonometric function may be written in terms of eix and e−ix, and then integrated. This technique is often simpler and faster than using trigonometric identities or integration by parts, and is sufficiently powerful to integrate any rational expression involving trigonometric functions. In integral calculus, complex numbers and Euler's formula may be used to evaluate integrals involving trigonometric functions. Using Euler's formula, any trigonometric function may be written in terms of eix and e−ix, and then integrated. This technique is often simpler and faster than using trigonometric identities or integration by parts, and is sufficiently powerful to integrate any rational expression involving trigonometric functions. Euler's formula states that Substituting −x for x gives the equation