\[ \int \frac {3+x^2}{\sqrt [3]{1+x^2} \left (-1-x^2+x^3\right )} \, dx \]
Optimal antiderivative \[ -\sqrt {3}\, \arctan \left (\frac {\frac {2 x \sqrt {3}}{3}+\frac {\left (x^{2}+1\right )^{\frac {1}{3}} \sqrt {3}}{3}}{\left (x^{2}+1\right )^{\frac {1}{3}}}\right )+\ln \left (-x +\left (x^{2}+1\right )^{\frac {1}{3}}\right )-\frac {\ln \left (x^{2}+x \left (x^{2}+1\right )^{\frac {1}{3}}+\left (x^{2}+1\right )^{\frac {2}{3}}\right )}{2} \]
command
Integrate[(3 + x^2)/((1 + x^2)^(1/3)*(-1 - x^2 + x^3)),x]
Mathematica 13.1 output
\[ -\sqrt {3} \text {ArcTan}\left (\frac {1+\frac {2 x}{\sqrt [3]{1+x^2}}}{\sqrt {3}}\right )+\log \left (-x+\sqrt [3]{1+x^2}\right )-\frac {1}{2} \log \left (x^2+x \sqrt [3]{1+x^2}+\left (1+x^2\right )^{2/3}\right ) \]
Mathematica 12.3 output
\[ \int \frac {3+x^2}{\sqrt [3]{1+x^2} \left (-1-x^2+x^3\right )} \, dx \]________________________________________________________________________________________