\[ \int \frac {e+f x}{x \sqrt {-1+x^3}} \, dx \]
Optimal antiderivative \[ \frac {2 e \arctan \left (\sqrt {x^{3}-1}\right )}{3}-\frac {2 f \left (1-x \right ) \EllipticF \left (\frac {1-x +\sqrt {3}}{1-x -\sqrt {3}}, 2 i-i \sqrt {3}\right ) \left (\frac {\sqrt {6}}{2}-\frac {\sqrt {2}}{2}\right ) \sqrt {\frac {x^{2}+x +1}{\left (1-x -\sqrt {3}\right )^{2}}}\, 3^{\frac {3}{4}}}{3 \sqrt {x^{3}-1}\, \sqrt {\frac {-1+x}{\left (1-x -\sqrt {3}\right )^{2}}}} \]
command
integrate((f*x+e)/x/(x^3-1)^(1/2),x, algorithm="fricas")
Fricas 1.3.8 (sbcl 2.2.11.debian) via sagemath 9.6 output
\[ \frac {1}{3} \, \arctan \left (\frac {x^{3} - 2}{2 \, \sqrt {x^{3} - 1}}\right ) e + 2 \, f {\rm weierstrassPInverse}\left (0, 4, x\right ) \]
Fricas 1.3.7 via sagemath 9.3 output
\[ {\rm integral}\left (\frac {\sqrt {x^{3} - 1} {\left (f x + e\right )}}{x^{4} - x}, x\right ) \]