 \textbf{1.} Spočtěte integrál
      $$
            \int \frac{dx}{x^2 + x - 2}.
      $$

      \textbf{Řešení}
      Použijeme faktu, že $1 = \frac 13 \bigl( (x+2) - (x-1) \bigr)$:
      \begin{multline*}
            \int \frac{dx}{x^2 + x - 2} = \frac13 \cdot
            \int \frac{(x+2) - (x-1)}{(x+2)(x-1)} \dx =\\
            =\frac 13 \cdot \int \left( \frac 1{x-1} - \frac1{x+2} \right) \dx \stackrel c=\\
            =\frac 13 \log\lvert x-1 \rvert - \frac 13 \log \lvert x+2 \rvert, \quad\text{na }
            (-\infty, -2) \cup (-2, 1) \cup (1, +\infty).
      \end{multline*}
