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{{more citations needed|date=July 2019}}
{{calculus|expanded=integral}}
In [[integral calculus]], [[Euler's formula]] for [[complex number]]s may be used to evaluate [[integral]]s involving [[trigonometric functions]]. Using Euler's formula, any trigonometric function may be written in terms of complex exponential functions, namely <math>e^{ix}</math> and <math>e^{-ix}</math> 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 fraction|rational expression]] involving trigonometric functions.<ref>{{Cite journal|last=Kilburn|first=Korey|title=Applying Euler's Formula to Integrate|journal=American Review of Mathematics and Statistics|date=2019 |publisher=American Research Institute for Policy Development|volume=7|pages=1–2|doi=10.15640/arms.v7n2a1|doi-broken-date=
==Euler's formula==
Euler's formula states that
:<math>e^{ix} = \cos x + i\,\sin x.</math>
Substituting <math>-x</math> for <math>x</math> gives the equation
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[[Category:Integral calculus]]
[[Category:Theorems in mathematical analysis]]
[[Category:Theorems in calculus]]
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