Example 8. Find the integral $\int \frac{d x}{\sqrt{3 x^{2}-6 x+9}}$.
Solution. As in example 7, we get

$$
\begin{gathered}
\int \frac{d x}{\sqrt{3 x^{2}-6 x+9}}=\int \frac{d x}{\sqrt{3\left(x^{2}-2 x+3\right)}}=\frac{1}{\sqrt{3}} \int \frac{d x}{\sqrt{\left(x^{2}-2 x+1\right)+2}}= \\
=\frac{1}{\sqrt{3}} \int \frac{d(x-1)}{\sqrt{(x-1)^{2}+2}}=\frac{1}{\sqrt{3}} \ln \left|(x-1)+\sqrt{(x-1)^{2}+2}\right|+C= \\
=\frac{1}{\sqrt{3}} \ln \left|x-1+\sqrt{x^{2}-2 x+3}\right|+C
\end{gathered}
$$