Example 7. Find the integral $\int \frac{d x}{\sqrt{x^{2}-6 x+3}}$.
Solution. By transforming the quadratic trinomial and applying formula (4.24), we find

$$
\begin{aligned}
\int \frac{d x}{\sqrt{x^{2}-6 x+3}} & =\int \frac{d x}{\sqrt{\left(x^{2}-6 x+9\right)-9+3}}=\int \frac{d(x-3)}{\sqrt{(x-3)^{2}-6}}= \\
= & \ln \left|(x-3)+\sqrt{(x-3)^{2}-6}\right|+C= \\
& =\ln \left|x-3+\sqrt{x^{2}-6 x+3}\right|+C
\end{aligned}
$$