\[ \int \frac {1}{\left (-1+x^2\right ) \sqrt [3]{-x+x^3}} \, dx \]
Optimal antiderivative \[ -\frac {3 \left (x^{3}-x \right )^{\frac {2}{3}}}{2 x^{2}-2} \]
command
integrate(1/(x^2-1)/(x^3-x)^(1/3),x, algorithm="fricas")
Fricas 1.3.8 (sbcl 2.2.11.debian) via sagemath 9.6 output
\[ -\frac {3 \, {\left (x^{3} - x\right )}^{\frac {2}{3}}}{2 \, {\left (x^{2} - 1\right )}} \]
Fricas 1.3.7 via sagemath 9.3 output
\[ \text {Timed out} \]