\[ \int \frac {c+d x^3+e x^6+f x^9}{x^7 \left (a+b x^3\right )} \, dx \]
Optimal antiderivative \[ -\frac {c}{6 a \,x^{6}}+\frac {-a d +b c}{3 a^{2} x^{3}}+\frac {\left (a^{2} e -a b d +b^{2} c \right ) \ln \! \left (x \right )}{a^{3}}-\frac {\left (-a^{3} f +a^{2} b e -a \,b^{2} d +b^{3} c \right ) \ln \! \left (b \,x^{3}+a \right )}{3 a^{3} b} \]
command
integrate((f*x**9+e*x**6+d*x**3+c)/x**7/(b*x**3+a),x)
Sympy 1.10.1 under Python 3.10.4 output
\[ \text {Timed out} \]
Sympy 1.8 under Python 3.8.8 output
\[ \frac {- a c + x^{3} \left (- 2 a d + 2 b c\right )}{6 a^{2} x^{6}} + \frac {\left (a^{2} e - a b d + b^{2} c\right ) \log {\left (x \right )}}{a^{3}} + \frac {\left (a^{3} f - a^{2} b e + a b^{2} d - b^{3} c\right ) \log {\left (\frac {a}{b} + x^{3} \right )}}{3 a^{3} b} \]