Integration using Euler's formula

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${\displaystyle \int _{a}^{b}f'(t)\,dt=f(b)-f(a)}$
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In integral calculus, Euler's formula for complex numbers may be used to evaluate integrals involving trigonometric functions. Using Euler's formula, any trigonometric function may be written in terms of complex exponential functions, namely ${\displaystyle e^{ix}}$ and ${\displaystyle e^{-ix}}$ 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.^[1]