**Evaluate**

** Solution.** First let us
complete the square
for . We get

which suggests the secant-substitution . Hence
we have and . Note that for *x*=0, we have which gives
*t*=0 and for *x*=3, we have which gives .
Therefore, we have

Using the trigonometric identities (you will find them at the end of this page), we get

The technique of integration related to the powers of the secant-function gives and

which implies

One would check easily that

Useful trigonometric identities:

**
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