\[ \int \frac {c+d x+e x^2+f x^3+g x^4+h x^5}{x^4 \left (a+b x^3\right )^3} \, dx \]
Optimal antiderivative \[ -\frac {c}{3 a^{3} x^{3}}-\frac {d}{2 a^{3} x^{2}}-\frac {e}{a^{3} x}-\frac {x \left (b d -a g +\left (-a h +b e \right ) x -b \left (\frac {b c}{a}-f \right ) x^{2}\right )}{6 a^{2} \left (b \,x^{3}+a \right )^{2}}-\frac {x \left (11 b d -5 a g +2 \left (-2 a h +5 b e \right ) x -3 b \left (\frac {5 b c}{a}-3 f \right ) x^{2}\right )}{18 a^{3} \left (b \,x^{3}+a \right )}-\frac {\left (-a f +3 b c \right ) \ln \left (x \right )}{a^{4}}-\frac {\left (5 b^{\frac {1}{3}} \left (-a g +4 b d \right )-2 a^{\frac {1}{3}} \left (-a h +7 b e \right )\right ) \ln \left (a^{\frac {1}{3}}+b^{\frac {1}{3}} x \right )}{27 a^{\frac {11}{3}} b^{\frac {2}{3}}}+\frac {\left (5 b^{\frac {1}{3}} \left (-a g +4 b d \right )-2 a^{\frac {1}{3}} \left (-a h +7 b e \right )\right ) \ln \left (a^{\frac {2}{3}}-a^{\frac {1}{3}} b^{\frac {1}{3}} x +b^{\frac {2}{3}} x^{2}\right )}{54 a^{\frac {11}{3}} b^{\frac {2}{3}}}+\frac {\left (-a f +3 b c \right ) \ln \left (b \,x^{3}+a \right )}{3 a^{4}}+\frac {\left (20 b^{\frac {4}{3}} d +14 a^{\frac {1}{3}} b e -5 a \,b^{\frac {1}{3}} g -2 a^{\frac {4}{3}} h \right ) \arctan \left (\frac {\left (a^{\frac {1}{3}}-2 b^{\frac {1}{3}} x \right ) \sqrt {3}}{3 a^{\frac {1}{3}}}\right ) \sqrt {3}}{27 a^{\frac {11}{3}} b^{\frac {2}{3}}} \]
command
integrate((h*x^5+g*x^4+f*x^3+e*x^2+d*x+c)/x^4/(b*x^3+a)^3,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 \[ \text {Timed out} \]