
  \textbf{2.} Spo�t�te ur�it� integr�l substituc�:
      $$
            \int_{-1}^{1} \frac{ x }{ \sqrt{5-4x} } dx.
      $$

      \textbf{�e�en�} Pou�ijeme substituci $\sqrt{5-4x} = t$:
      \begin{align*}
            \sqrt{5-4x} &= t\\
            5 - 4x            &= t^2\\
            x           &= \frac 54 - \frac{t^2}4\\
            dx          &= -\frac t2 dt
      \end{align*}
      Dost�v�me:
      \begin{multline*}
            \int_{-1}^{1} \frac{ x }{ \sqrt{5-4x} } dx \subst
            \int_3^1 \frac{ \frac54 - \frac{t^2}4 }{ t } \cdot \left( -\frac t2 \right) dt =
            \int_3^1 \left( \frac{t^2}8 - \frac 58 \right) dt =\\
            =\left[ \frac{t^3}{24} - \frac{5t}8 \right]_3^1 =
            \frac{1}{24} - \frac{5}{8} - \frac{3^3}{24} + \frac{15}{8} =
            \frac{1 - 15 - 27 + 45}{24} = \frac16.
      \end{multline*}
