 \textbf{5.} Spočtěte integrál
      $$
            \int \left(\frac ax + \frac{a^2}{x^2} + \frac {a^3}{x^3}\right) \dx
      $$
      \textbf{Řešení}
      \begin{multline*}
            \int \left(\frac ax + \frac{a^2}{x^2} + \frac {a^3}{x^3}\right) \dx =
            \int \frac ax \dx + \int \frac{a^2}{x^2} \dx + \int \frac{a^3}{x^3} \dx \stackrel c=\\
            =
            a\ln |x| - \frac{a^2}x + a^3 \cdot \int x^{-3} \dx \stackrel c=
            a\ln |x| - \frac{a^2}x - \frac{a^3}{2x^2}.
      \end{multline*}
