
      \textbf{5.} Spo�t�te integr�l
      $$
            \int_{-\infty}^{+\infty} \frac{dx}{1 + x^2}.
      $$

      \textbf{�e�en�}
      $$
            \int_{-\infty}^{+\infty} \frac{dx}{1 + x^2} =
            [\arctg x]_{-\infty}^{+\infty} =
            \lim_{x\to+\infty} \arctg x - \lim_{x\to-\infty} \arctg x =
            \frac{\pi}{2} - \left(-\frac{\pi}{2}\right) = \pi.
      $$
