\[ \int \frac {c+d x^3+e x^6+f x^9}{x \left (a+b x^3\right )^2} \, dx \]
Optimal antiderivative \[ \frac {f \,x^{3}}{3 b^{2}}+\frac {-a^{3} f +a^{2} b e -a \,b^{2} d +b^{3} c}{3 a \,b^{3} \left (b \,x^{3}+a \right )}+\frac {c \ln \! \left (x \right )}{a^{2}}-\frac {\left (2 a^{3} f -a^{2} b e +b^{3} c \right ) \ln \! \left (b \,x^{3}+a \right )}{3 a^{2} b^{3}} \]
command
integrate((f*x**9+e*x**6+d*x**3+c)/x/(b*x**3+a)**2,x)
Sympy 1.10.1 under Python 3.10.4 output
\[ \text {Timed out} \]
Sympy 1.8 under Python 3.8.8 output
\[ \frac {- a^{3} f + a^{2} b e - a b^{2} d + b^{3} c}{3 a^{2} b^{3} + 3 a b^{4} x^{3}} + \frac {f x^{3}}{3 b^{2}} + \frac {c \log {\left (x \right )}}{a^{2}} - \frac {\left (2 a^{3} f - a^{2} b e + b^{3} c\right ) \log {\left (\frac {a}{b} + x^{3} \right )}}{3 a^{2} b^{3}} \]