\[ \int \frac {c+d x+e x^2+f x^3+g x^4+h x^5}{x^3 \left (a+b x^3\right )} \, dx \]
Optimal antiderivative \[ -\frac {c}{2 a \,x^{2}}-\frac {d}{a x}+\frac {e \ln \left (x \right )}{a}-\frac {\left (b^{\frac {1}{3}} \left (-a f +b c \right )-a^{\frac {1}{3}} \left (-a g +b d \right )\right ) \ln \left (a^{\frac {1}{3}}+b^{\frac {1}{3}} x \right )}{3 a^{\frac {5}{3}} b^{\frac {2}{3}}}+\frac {\left (b^{\frac {1}{3}} \left (-a f +b c \right )-a^{\frac {1}{3}} \left (-a g +b d \right )\right ) \ln \left (a^{\frac {2}{3}}-a^{\frac {1}{3}} b^{\frac {1}{3}} x +b^{\frac {2}{3}} x^{2}\right )}{6 a^{\frac {5}{3}} b^{\frac {2}{3}}}-\frac {\left (-a h +b e \right ) \ln \left (b \,x^{3}+a \right )}{3 a b}+\frac {\left (b^{\frac {4}{3}} c +a^{\frac {1}{3}} b d -a \,b^{\frac {1}{3}} f -a^{\frac {4}{3}} g \right ) \arctan \left (\frac {\left (a^{\frac {1}{3}}-2 b^{\frac {1}{3}} x \right ) \sqrt {3}}{3 a^{\frac {1}{3}}}\right ) \sqrt {3}}{3 a^{\frac {5}{3}} b^{\frac {2}{3}}} \]
command
integrate((h*x^5+g*x^4+f*x^3+e*x^2+d*x+c)/x^3/(b*x^3+a),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 \[ \text {Timed out} \]