# Trigonometric substitution

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Integration by trigonometric substitution is a technique of integration that involves making a change of variables for example normally one would change from the variable x to theta.

Examples: Compute $\int \sqrt{1-x^2} dx$
For this problem it seems wise to let $x=\sin{\theta},dx=\cos{\theta}d\theta$
Now with this substitution we have: $\int \sqrt{1-\sin^2{\theta}}\cos{\theta}d\theta$
By the trigonometric identity $\sin^2{x}+\cos^2{x}=1$ we now have:
$\sqrt{1-\sin^2{\theta}}=\cos{\theta}$
Therefore:
$\int \cos^2{\theta} d\theta$