The familiar trigonometric identities

may be used to eliminate radicals from integrals. Specially when these integrals involve and .

**1**- For set . In this case we talk about sine-substitution.
**2**- For set . In this case we talk about tangent-substitution.
**3**- For set . In this case we
talk about secant-substitution.

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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