
      \textbf{4.} Spočtěte integrál
      $$
            \int \left(\frac{x-1}{x}\right)^2 \dx.
      $$

      \textbf{Řešení}
      $$
            \int \left(\frac{x-1}{x}\right)^2 \dx = \int \frac{x^2 - 2x + 1}{x^2} \dx =
            \int \left( 1 - \frac 2x + \frac 1{x^2} \right) \dx \stackrel c=
            x - 2\ln |x| - \frac 1x.
      $$
