Ta có:
$\int\limits_0^1\dfrac{x^3}{x^4+3x^2+2}dx$
$=\int\limits_0^1\left(\dfrac{2x}{x^2+2}-\dfrac{x}{x^2+1}\right)dx$
$=\int\limits_0^1\dfrac{d(x^2+2)}{x^2+2}-\dfrac{1}{2}\int\limits_0^1\dfrac{d(x^2+1)}{x^2+1}$
$=\left(\ln(x^2+2)-\dfrac{1}{2}\ln(x^2+1)\right)\left|\begin{array}{l}1\\0\end{array}\right.$
$=\ln3-\dfrac{\ln2}{2}$