Consider functions of the form
where is a real variable and are real-valued
functions. For example,
We observed before that
For example, writing it as in (5.2.2),
. Wouldn't it be nice if
we could just write
? This is useless for us though,
since we haven't even defined
However, we can ``rationalize the denominator'' by writing
This informs how we would define
you'll do if you take a course in complex analysis).
in the numerator.
The next example illustrates an alternative to the method
of Section 5.2.
more tedious than the method in 5.2
But it is completely straightforward
. You don't need
any trig formulas or anything else. You just multiply it out,
integrate, etc., and remember that