\[ \int \frac {1}{x^3 \sqrt {1-x^3}} \, dx \]
Optimal antiderivative \[ -\frac {\sqrt {-x^{3}+1}}{2 x^{2}}-\frac {\left (1-x \right ) \EllipticF \left (\frac {1-x -\sqrt {3}}{1-x +\sqrt {3}}, i \sqrt {3}+2 i\right ) \left (\frac {\sqrt {6}}{2}+\frac {\sqrt {2}}{2}\right ) \sqrt {\frac {x^{2}+x +1}{\left (1-x +\sqrt {3}\right )^{2}}}\, 3^{\frac {3}{4}}}{6 \sqrt {-x^{3}+1}\, \sqrt {\frac {1-x}{\left (1-x +\sqrt {3}\right )^{2}}}} \]
command
integrate(1/x^3/(-x^3+1)^(1/2),x, algorithm="fricas")
Fricas 1.3.8 (sbcl 2.2.11.debian) via sagemath 9.6 output
\[ -\frac {\sqrt {-x^{3} + 1}}{2 \, x^{2}} \]
Fricas 1.3.7 via sagemath 9.3 output
\[ {\rm integral}\left (-\frac {\sqrt {-x^{3} + 1}}{x^{6} - x^{3}}, x\right ) \]