Example 2. Find the integral $\int \frac{d x}{x^{2}-6 x-16}$.
Solution. Completing the square trinomial to a perfect square and integrating based on formula (4.20) for the case when $u=x-3$, $a=5$, we get

$$
\begin{aligned}
& \int \frac{d x}{x^{2}-6 x-16}=\int \frac{d x}{\left(x^{2}-6 x+9\right)-9-16}=\int \frac{d x}{(x-3)^{2}-25}= \\
= & \int \frac{d(x-3)}{(x-3)^{2}-5^{2}}=\frac{1}{2 \cdot 5} \ln \left|\frac{(x-3)-5}{(x-3)+5}\right|+C=\frac{1}{10} \ln \left|\frac{x-8}{x+2}\right|+C
\end{aligned}
$$