The familiar trigonometric identities
may be used to eliminate radicals from integrals. Specially when these integrals involve and .
The expressions and should be seen as a constant plus-minus a square of a function. In this case, x represents a function and a a constant. For example can be seen as one of the two previous expressions. Indeed, if we complete the square we get
where . So from the above substitutions, we will set .
The following examples illustrate how to use trigonometric substitutions :
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Author: Mohamed Amine Khamsi