\[ \int \frac {x}{\sqrt {a-b x^3} \left (2 \left (5+3 \sqrt {3}\right ) a-b x^3\right )} \, dx \]
Optimal antiderivative \[ -\frac {\arctan \left (\frac {3^{\frac {1}{4}} a^{\frac {1}{6}} \left (a^{\frac {1}{3}}-b^{\frac {1}{3}} x \right ) \left (1+\sqrt {3}\right ) \sqrt {2}}{2 \sqrt {-b \,x^{3}+a}}\right ) \left (2-\sqrt {3}\right ) 3^{\frac {1}{4}} \sqrt {2}}{12 a^{\frac {5}{6}} b^{\frac {2}{3}}}-\frac {\arctan \left (\frac {\left (1-\sqrt {3}\right ) \sqrt {-b \,x^{3}+a}\, 3^{\frac {1}{4}} \sqrt {2}}{6 \sqrt {a}}\right ) \left (2-\sqrt {3}\right ) 3^{\frac {1}{4}} \sqrt {2}}{18 a^{\frac {5}{6}} b^{\frac {2}{3}}}-\frac {\arctanh \left (\frac {3^{\frac {1}{4}} a^{\frac {1}{6}} \left (a^{\frac {1}{3}}-b^{\frac {1}{3}} x \right ) \left (1-\sqrt {3}\right ) \sqrt {2}}{2 \sqrt {-b \,x^{3}+a}}\right ) \left (2-\sqrt {3}\right ) 3^{\frac {3}{4}} \sqrt {2}}{36 a^{\frac {5}{6}} b^{\frac {2}{3}}}-\frac {\arctanh \left (\frac {3^{\frac {1}{4}} a^{\frac {1}{6}} \left (2 b^{\frac {1}{3}} x +a^{\frac {1}{3}} \left (1+\sqrt {3}\right )\right ) \sqrt {2}}{2 \sqrt {-b \,x^{3}+a}}\right ) \left (2-\sqrt {3}\right ) 3^{\frac {3}{4}} \sqrt {2}}{18 a^{\frac {5}{6}} b^{\frac {2}{3}}} \]
command
integrate(x/(-b*x^3+2*a*(5+3*3^(1/2)))/(-b*x^3+a)^(1/2),x, algorithm="fricas")
Fricas 1.3.8 (sbcl 2.2.11.debian) via sagemath 9.6 output
\[ \text {output too large to display} \]
Fricas 1.3.7 via sagemath 9.3 output \[ \text {Exception raised: TypeError} \]