\[ \int \frac {x}{(2+x) \sqrt {1-x^3}} \, dx \]
Optimal antiderivative \[ \frac {4 \arctanh \left (\frac {\left (1-x \right )^{2}}{3 \sqrt {-x^{3}+1}}\right )}{9}-\frac {2 \left (1-x \right ) \EllipticF \left (\frac {1-x -\sqrt {3}}{1-x +\sqrt {3}}, i \sqrt {3}+2 i\right ) \left (\frac {\sqrt {6}}{2}+\frac {\sqrt {2}}{2}\right ) \sqrt {\frac {x^{2}+x +1}{\left (1-x +\sqrt {3}\right )^{2}}}\, 3^{\frac {3}{4}}}{9 \sqrt {-x^{3}+1}\, \sqrt {\frac {1-x}{\left (1-x +\sqrt {3}\right )^{2}}}} \]
command
integrate(x/(2+x)/(-x^3+1)^(1/2),x, algorithm="fricas")
Fricas 1.3.8 (sbcl 2.2.11.debian) via sagemath 9.6 output
\[ \frac {2}{9} \, \log \left (-\frac {x^{3} - 12 \, x^{2} + 6 \, \sqrt {-x^{3} + 1} {\left (x - 1\right )} - 6 \, x - 10}{x^{3} + 6 \, x^{2} + 12 \, x + 8}\right ) \]
Fricas 1.3.7 via sagemath 9.3 output
\[ {\rm integral}\left (-\frac {\sqrt {-x^{3} + 1} x}{x^{4} + 2 \, x^{3} - x - 2}, x\right ) \]