= Trigonometric substitution
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A <trigonometric substitution> is <integration by substitution> using a <trigonometric function> to simplify an integrand, especially a square root. For example, $x=a\sin u$, with $a>0$ and $-\pi/2\le u\le\pi/2$, changes $\sqrt{a^2-x^2}$ to $a\cos u$ and $dx$ to $a\cos u\,du$. The interval restriction fixes the sign of the square root. Similarly $x=a\tan u$ simplifies $\sqrt{a^2+x^2}$. The transformed <integral> must include the differential and, for a <definite integral>, the new limits.
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