\[ \int \frac {x \left (c+d x+e x^2+f x^3+g x^4+h x^5\right )}{a+b x^3} \, dx \]
Optimal antiderivative \[ \frac {\left (-a h +b e \right ) x}{b^{2}}+\frac {f \,x^{2}}{2 b}+\frac {g \,x^{3}}{3 b}+\frac {h \,x^{4}}{4 b}-\frac {\left (b^{\frac {2}{3}} \left (-a f +b c \right )+a^{\frac {2}{3}} \left (-a h +b e \right )\right ) \ln \left (a^{\frac {1}{3}}+b^{\frac {1}{3}} x \right )}{3 a^{\frac {1}{3}} b^{\frac {7}{3}}}+\frac {\left (b^{\frac {2}{3}} \left (-a f +b c \right )+a^{\frac {2}{3}} \left (-a h +b e \right )\right ) \ln \left (a^{\frac {2}{3}}-a^{\frac {1}{3}} b^{\frac {1}{3}} x +b^{\frac {2}{3}} x^{2}\right )}{6 a^{\frac {1}{3}} b^{\frac {7}{3}}}+\frac {\left (-a g +b d \right ) \ln \left (b \,x^{3}+a \right )}{3 b^{2}}-\frac {\left (b^{\frac {5}{3}} c -a^{\frac {2}{3}} b e -a \,b^{\frac {2}{3}} f +a^{\frac {5}{3}} h \right ) \arctan \left (\frac {\left (a^{\frac {1}{3}}-2 b^{\frac {1}{3}} x \right ) \sqrt {3}}{3 a^{\frac {1}{3}}}\right ) \sqrt {3}}{3 a^{\frac {1}{3}} b^{\frac {7}{3}}} \]
command
integrate(x*(h*x^5+g*x^4+f*x^3+e*x^2+d*x+c)/(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 \[ \text {Timed out} \]