\[ \int \frac {\left (2+5 x^7\right ) \sqrt [3]{-x-x^3+x^8}}{\left (-1+x^7\right ) \left (-1+x^2+x^7\right )} \, dx \]
Optimal antiderivative \[ \sqrt {3}\, \arctan \left (\frac {\sqrt {3}\, x}{-x +2 \left (x^{8}-x^{3}-x \right )^{\frac {1}{3}}}\right )-2^{\frac {1}{3}} \sqrt {3}\, \arctan \left (\frac {\sqrt {3}\, x}{-x +2^{\frac {2}{3}} \left (x^{8}-x^{3}-x \right )^{\frac {1}{3}}}\right )-\ln \left (x +\left (x^{8}-x^{3}-x \right )^{\frac {1}{3}}\right )+2^{\frac {1}{3}} \ln \left (2 x +2^{\frac {2}{3}} \left (x^{8}-x^{3}-x \right )^{\frac {1}{3}}\right )+\frac {\ln \left (x^{2}-x \left (x^{8}-x^{3}-x \right )^{\frac {1}{3}}+\left (x^{8}-x^{3}-x \right )^{\frac {2}{3}}\right )}{2}-\frac {\ln \left (-2 x^{2}+2^{\frac {2}{3}} x \left (x^{8}-x^{3}-x \right )^{\frac {1}{3}}-2^{\frac {1}{3}} \left (x^{8}-x^{3}-x \right )^{\frac {2}{3}}\right ) 2^{\frac {1}{3}}}{2} \]
command
Integrate[((2 + 5*x^7)*(-x - x^3 + x^8)^(1/3))/((-1 + x^7)*(-1 + x^2 + x^7)),x]
Mathematica 13.1 output
\[ \frac {x^{2/3} \left (-1-x^2+x^7\right )^{2/3} \left (-2 \sqrt {3} \text {ArcTan}\left (\frac {\sqrt {3} x^{2/3}}{x^{2/3}-2 \sqrt [3]{-1-x^2+x^7}}\right )+2 \sqrt [3]{2} \sqrt {3} \text {ArcTan}\left (\frac {\sqrt {3} x^{2/3}}{x^{2/3}-2^{2/3} \sqrt [3]{-1-x^2+x^7}}\right )-2 \log \left (x^{2/3}+\sqrt [3]{-1-x^2+x^7}\right )+2 \sqrt [3]{2} \log \left (2 x^{2/3}+2^{2/3} \sqrt [3]{-1-x^2+x^7}\right )+\log \left (x^{4/3}-x^{2/3} \sqrt [3]{-1-x^2+x^7}+\left (-1-x^2+x^7\right )^{2/3}\right )-\sqrt [3]{2} \log \left (-2 x^{4/3}+2^{2/3} x^{2/3} \sqrt [3]{-1-x^2+x^7}-\sqrt [3]{2} \left (-1-x^2+x^7\right )^{2/3}\right )\right )}{2 \left (x \left (-1-x^2+x^7\right )\right )^{2/3}} \]
Mathematica 12.3 output
\[ \text {\$Aborted} \]________________________________________________________________________________________