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