\(\begin{array}{l}
\quad x(x^2 + 1)dx - (x+1)ydy = 0\\
\Leftrightarrow ydy = \dfrac{x^3+x}{x+1}dx\\
\Leftrightarrow \displaystyle\int ydy = \displaystyle\int\dfrac{x^3+x}{x+1}dx\\
\Leftrightarrow \dfrac{y^2}{2} = \dfrac{x^3}{3} - \dfrac{x^2}{2} + 2x - 2\ln(x+1) + C\\
\Leftrightarrow y = \pm \sqrt{\dfrac{2x^3}{3} - x^2 + 4x - 4\ln(x+1) + C'}
\end{array}\)