\[ \int \frac {1}{(a+b x)^3 (c+d x)^8} \, dx \]
Optimal antiderivative \[ -\frac {b^{7}}{2 \left (-a d +b c \right )^{8} \left (b x +a \right )^{2}}+\frac {8 b^{7} d}{\left (-a d +b c \right )^{9} \left (b x +a \right )}+\frac {d^{2}}{7 \left (-a d +b c \right )^{3} \left (d x +c \right )^{7}}+\frac {b \,d^{2}}{2 \left (-a d +b c \right )^{4} \left (d x +c \right )^{6}}+\frac {6 b^{2} d^{2}}{5 \left (-a d +b c \right )^{5} \left (d x +c \right )^{5}}+\frac {5 b^{3} d^{2}}{2 \left (-a d +b c \right )^{6} \left (d x +c \right )^{4}}+\frac {5 b^{4} d^{2}}{\left (-a d +b c \right )^{7} \left (d x +c \right )^{3}}+\frac {21 b^{5} d^{2}}{2 \left (-a d +b c \right )^{8} \left (d x +c \right )^{2}}+\frac {28 b^{6} d^{2}}{\left (-a d +b c \right )^{9} \left (d x +c \right )}+\frac {36 b^{7} d^{2} \ln \! \left (b x +a \right )}{\left (-a d +b c \right )^{10}}-\frac {36 b^{7} d^{2} \ln \! \left (d x +c \right )}{\left (-a d +b c \right )^{10}} \]
command
integrate(1/(b*x+a)**3/(d*x+c)**8,x)
Sympy 1.10.1 under Python 3.10.4 output
\[ \text {Timed out} \]
Sympy 1.8 under Python 3.8.8 output
\[ \text {output too large to display} \]