\[ \int \frac {(c i+d i x)^3 \left (A+B \log \left (\frac {e (a+b x)}{c+d x}\right )\right )^2}{(a g+b g x)^7} \, dx \]
Optimal antiderivative \[ -\frac {B^{2} d^{2} i^{3} \left (d x +c \right )^{4}}{32 \left (-a d +b c \right )^{3} g^{7} \left (b x +a \right )^{4}}+\frac {4 b \,B^{2} d \,i^{3} \left (d x +c \right )^{5}}{125 \left (-a d +b c \right )^{3} g^{7} \left (b x +a \right )^{5}}-\frac {b^{2} B^{2} i^{3} \left (d x +c \right )^{6}}{108 \left (-a d +b c \right )^{3} g^{7} \left (b x +a \right )^{6}}-\frac {B \,d^{2} i^{3} \left (d x +c \right )^{4} \left (A +B \ln \left (\frac {e \left (b x +a \right )}{d x +c}\right )\right )}{8 \left (-a d +b c \right )^{3} g^{7} \left (b x +a \right )^{4}}+\frac {4 b B d \,i^{3} \left (d x +c \right )^{5} \left (A +B \ln \left (\frac {e \left (b x +a \right )}{d x +c}\right )\right )}{25 \left (-a d +b c \right )^{3} g^{7} \left (b x +a \right )^{5}}-\frac {b^{2} B \,i^{3} \left (d x +c \right )^{6} \left (A +B \ln \left (\frac {e \left (b x +a \right )}{d x +c}\right )\right )}{18 \left (-a d +b c \right )^{3} g^{7} \left (b x +a \right )^{6}}-\frac {d^{2} i^{3} \left (d x +c \right )^{4} \left (A +B \ln \left (\frac {e \left (b x +a \right )}{d x +c}\right )\right )^{2}}{4 \left (-a d +b c \right )^{3} g^{7} \left (b x +a \right )^{4}}+\frac {2 b d \,i^{3} \left (d x +c \right )^{5} \left (A +B \ln \left (\frac {e \left (b x +a \right )}{d x +c}\right )\right )^{2}}{5 \left (-a d +b c \right )^{3} g^{7} \left (b x +a \right )^{5}}-\frac {b^{2} i^{3} \left (d x +c \right )^{6} \left (A +B \ln \left (\frac {e \left (b x +a \right )}{d x +c}\right )\right )^{2}}{6 \left (-a d +b c \right )^{3} g^{7} \left (b x +a \right )^{6}} \]
command
integrate((d*i*x+c*i)^3*(A+B*log(e*(b*x+a)/(d*x+c)))^2/(b*g*x+a*g)^7,x, algorithm="maxima")
Maxima 5.46 SBCL 2.0.1.debian via sagemath 9.6 output
\[ \text {output too large to display} \]
Maxima 5.44 via sagemath 9.3 output \[ \text {Timed out} \]_____________________________________________________