\[ \int \frac {\left (3+x^2\right ) \left (1+x^2+x^3\right )^{2/3}}{-1-2 x^2+x^3-x^4+x^5+x^6} \, dx \]
Optimal antiderivative \[ \mathit {Unintegrable} \]
command
Integrate[((3 + x^2)*(1 + x^2 + x^3)^(2/3))/(-1 - 2*x^2 + x^3 - x^4 + x^5 + x^6),x]
Mathematica 13.1 output
\[ \text {RootSum}\left [1-3 \text {$\#$1}^3+\text {$\#$1}^6\&,\frac {-\log (x) \text {$\#$1}^2+\log \left (\sqrt [3]{1+x^2+x^3}-x \text {$\#$1}\right ) \text {$\#$1}^2}{-3+2 \text {$\#$1}^3}\&\right ] \]
Mathematica 12.3 output
\[ \int \frac {\left (3+x^2\right ) \left (1+x^2+x^3\right )^{2/3}}{-1-2 x^2+x^3-x^4+x^5+x^6} \, dx \]________________________________________________________________________________________