\[ \int \frac {1}{\sqrt [3]{2+3 x^2} \left (6 d+d x^2\right )} \, dx \]
Optimal antiderivative \[ -\frac {\arctanh \left (\frac {2^{\frac {1}{6}} \left (2^{\frac {1}{3}}-\left (3 x^{2}+2\right )^{\frac {1}{3}}\right )}{x}\right ) 2^{\frac {1}{6}}}{8 d}+\frac {\arctan \left (\frac {\left (2^{\frac {1}{3}}-\left (3 x^{2}+2\right )^{\frac {1}{3}}\right )^{2} 2^{\frac {5}{6}} \sqrt {3}}{18 x}\right ) 2^{\frac {1}{6}} \sqrt {3}}{24 d}+\frac {\arctan \left (\frac {x \sqrt {6}}{6}\right ) 2^{\frac {1}{6}} \sqrt {3}}{24 d} \]
command
integrate(1/(3*x^2+2)^(1/3)/(d*x^2+6*d),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 \[ \text {Timed out} \]