\[ \int \frac {e^{-a-b x} (a+b x)^4}{(c+d x)^5} \, dx \]
Optimal antiderivative \[ -\frac {\left (-a d +b c \right )^{4} {\mathrm e}^{-b x -a}}{4 d^{5} \left (d x +c \right )^{4}}+\frac {4 b \left (-a d +b c \right )^{3} {\mathrm e}^{-b x -a}}{3 d^{5} \left (d x +c \right )^{3}}+\frac {b \left (-a d +b c \right )^{4} {\mathrm e}^{-b x -a}}{12 d^{6} \left (d x +c \right )^{3}}-\frac {3 b^{2} \left (-a d +b c \right )^{2} {\mathrm e}^{-b x -a}}{d^{5} \left (d x +c \right )^{2}}-\frac {2 b^{2} \left (-a d +b c \right )^{3} {\mathrm e}^{-b x -a}}{3 d^{6} \left (d x +c \right )^{2}}-\frac {b^{2} \left (-a d +b c \right )^{4} {\mathrm e}^{-b x -a}}{24 d^{7} \left (d x +c \right )^{2}}+\frac {4 b^{3} \left (-a d +b c \right ) {\mathrm e}^{-b x -a}}{d^{5} \left (d x +c \right )}+\frac {3 b^{3} \left (-a d +b c \right )^{2} {\mathrm e}^{-b x -a}}{d^{6} \left (d x +c \right )}+\frac {2 b^{3} \left (-a d +b c \right )^{3} {\mathrm e}^{-b x -a}}{3 d^{7} \left (d x +c \right )}+\frac {b^{3} \left (-a d +b c \right )^{4} {\mathrm e}^{-b x -a}}{24 d^{8} \left (d x +c \right )}+\frac {b^{4} {\mathrm e}^{-a +\frac {b c}{d}} \expIntegral \left (-\frac {b \left (d x +c \right )}{d}\right )}{d^{5}}+\frac {4 b^{4} \left (-a d +b c \right ) {\mathrm e}^{-a +\frac {b c}{d}} \expIntegral \left (-\frac {b \left (d x +c \right )}{d}\right )}{d^{6}}+\frac {3 b^{4} \left (-a d +b c \right )^{2} {\mathrm e}^{-a +\frac {b c}{d}} \expIntegral \left (-\frac {b \left (d x +c \right )}{d}\right )}{d^{7}}+\frac {2 b^{4} \left (-a d +b c \right )^{3} {\mathrm e}^{-a +\frac {b c}{d}} \expIntegral \left (-\frac {b \left (d x +c \right )}{d}\right )}{3 d^{8}}+\frac {b^{4} \left (-a d +b c \right )^{4} {\mathrm e}^{-a +\frac {b c}{d}} \expIntegral \left (-\frac {b \left (d x +c \right )}{d}\right )}{24 d^{9}} \]
command
integrate(exp(-b*x-a)*(b*x+a)^4/(d*x+c)^5,x, algorithm="giac")
Giac 1.9.0-11 via sagemath 9.6 output
\[ \text {output too large to display} \]
Giac 1.7.0 via sagemath 9.3 output \[ \text {Timed out} \]_______________________________________________________