Example 2.26. $\int_{-\infty}^{+\infty} \frac{d x}{x^{2}+6 x+18}$.
Solution. Apply formula (2.7)

$$
\int_{-\infty}^{+\infty} \frac{d x}{x^{2}+6 x+18}=\lim _{\substack{a \rightarrow-\infty \\ b \rightarrow \infty}} \int_{a}^{b} \frac{d x}{x^{2}+6 x+18}=
$$

$$
=\lim _{\substack{a \rightarrow-\infty \\ b \rightarrow \infty}} \int_{a}^{b} \frac{d x}{(x+3)^{2}+9}=\left.\lim _{\substack{a \rightarrow-\infty \\ b \rightarrow \infty}} \frac{1}{3} \operatorname{arctg}\left(\frac{x+3}{3}\right)\right|_{a} ^{b}=\frac{\pi}{3} .
$$