Obliczamy całkę metodą podstawiania: \[ \begin{split} \int\frac{-5x}{\sqrt[3]{x^2 +2}}dx &=\begin{vmatrix} t=x^2+2 \\ dt = 2xdx \\ dx= \frac{dt}{2x}\end{vmatrix}=\\[6pt] &=\int\frac{-5x}{\sqrt[3]{t}}\frac{dt}{2x}=\\[6pt] &=\int \frac{-5dt}{2\sqrt[3]{t}}=\\[6pt] &=-\frac{5}{2}\int t^{-\frac{1}{3}}dt=\\[6pt] &=-\frac{5}{2}\cdot \frac{3}{2}t^{\frac{2}{3}}+C=\\[6pt] &=-\frac{15}{4}t^{\frac{2}{3}}+C=\\[6pt] &=-\frac{15}{4}\left ( x^2+2 \right )^{\frac{2}{3}}+C \end{split} \]