\[ \int \frac {2+3 x}{\left (2^{2/3}-x\right ) \sqrt {1-x^3}} \, dx \]
Optimal antiderivative \[ -\frac {2 \left (2+3 \,2^{\frac {2}{3}}\right ) \arctan \left (\frac {\left (1-2^{\frac {1}{3}} x \right ) \sqrt {3}}{\sqrt {-x^{3}+1}}\right ) \sqrt {3}}{9}+\frac {2 \left (3-2 \,2^{\frac {1}{3}}\right ) \left (1-x \right ) \EllipticF \left (\frac {1-x -\sqrt {3}}{1-x +\sqrt {3}}, i \sqrt {3}+2 i\right ) \left (\frac {\sqrt {6}}{2}+\frac {\sqrt {2}}{2}\right ) \sqrt {\frac {x^{2}+x +1}{\left (1-x +\sqrt {3}\right )^{2}}}\, 3^{\frac {3}{4}}}{9 \sqrt {-x^{3}+1}\, \sqrt {\frac {1-x}{\left (1-x +\sqrt {3}\right )^{2}}}} \]
command
integrate((2+3*x)/(2^(2/3)-x)/(-x^3+1)^(1/2),x, algorithm="fricas")
Fricas 1.3.8 (sbcl 2.2.11.debian) via sagemath 9.6 output
\[ -\frac {1}{9} \, \sqrt {3} \sqrt {12 \cdot 2^{\frac {2}{3}} + 18 \cdot 2^{\frac {1}{3}} + 4} \arctan \left (\frac {\sqrt {3} {\left (18 \, x^{5} - 42 \, x^{4} - 10 \, x^{3} - 18 \, x^{2} + 2^{\frac {2}{3}} {\left (2 \, x^{5} + 63 \, x^{4} + 15 \, x^{3} - 2 \, x^{2} - 36 \, x - 6\right )} - 2^{\frac {1}{3}} {\left (6 \, x^{5} - 14 \, x^{4} + 45 \, x^{3} - 6 \, x^{2} + 8 \, x - 18\right )} + 24 \, x + 4\right )} \sqrt {-x^{3} + 1} \sqrt {12 \cdot 2^{\frac {2}{3}} + 18 \cdot 2^{\frac {1}{3}} + 4}}{348 \, {\left (2 \, x^{6} - 3 \, x^{3} + 1\right )}}\right ) \]
Fricas 1.3.7 via sagemath 9.3 output
\[ {\rm integral}\left (\frac {{\left (3 \, x^{3} + 2 \, x^{2} + 2^{\frac {2}{3}} {\left (3 \, x^{2} + 2 \, x\right )} + 2 \cdot 2^{\frac {1}{3}} {\left (3 \, x + 2\right )}\right )} \sqrt {-x^{3} + 1}}{x^{6} - 5 \, x^{3} + 4}, x\right ) \]