Inverses
Trigonometric Substitutions
Trigonometric substitutions replace the binomials
,
, 
by single squared terms, so square roots can be simplified and integrals
can be evaluated directly.
Three Basic Substitutions
The substitutions replaces a function of
by a function of 
.In order to get the answer to the integral problem back in terms of
,we need the above trigonometric substitutions to be reversible.
The substitutions must have inverses.
The inverses exist under the following conditions:
requires
requires
requires
.See Examples 1 - 4, pages 566 - 569.
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