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Integration using Euler's formula : ウィキペディア英語版
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 ''e''''ix'' 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==
Euler's formula states that
:e^ = \cos x + i\,\sin x.
Substituting −''x'' for ''x'' gives the equation
:e^ = \cos x - i\,\sin x.
These two equations can be solved for the sine and cosine:
:\cos x = \frac}\quad\text\quad\sin x = \frac}.

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