\[ \int \frac {-3+x^4}{\sqrt [3]{1+x^4} \left (1-x^3+x^4\right )} \, dx \]
Optimal antiderivative \[ -\sqrt {3}\, \arctan \left (\frac {\sqrt {3}\, x}{x +2 \left (x^{4}+1\right )^{\frac {1}{3}}}\right )+\ln \left (-x +\left (x^{4}+1\right )^{\frac {1}{3}}\right )-\frac {\ln \left (x^{2}+x \left (x^{4}+1\right )^{\frac {1}{3}}+\left (x^{4}+1\right )^{\frac {2}{3}}\right )}{2} \]
command
Integrate[(-3 + x^4)/((1 + x^4)^(1/3)*(1 - x^3 + x^4)),x]
Mathematica 13.1 output
\[ -\sqrt {3} \text {ArcTan}\left (\frac {\sqrt {3} x}{x+2 \sqrt [3]{1+x^4}}\right )+\log \left (-x+\sqrt [3]{1+x^4}\right )-\frac {1}{2} \log \left (x^2+x \sqrt [3]{1+x^4}+\left (1+x^4\right )^{2/3}\right ) \]
Mathematica 12.3 output
\[ \int \frac {-3+x^4}{\sqrt [3]{1+x^4} \left (1-x^3+x^4\right )} \, dx \]________________________________________________________________________________________