\[ \int \frac {\log \left (\frac {d (a+b x)}{b (c+d x)}\right )}{c f+d f x} \, dx \]
Optimal antiderivative \[ \frac {\polylog \left (2, \frac {-a d +b c}{b \left (d x +c \right )}\right )}{d f} \]
command
integrate(log(d*(b*x+a)/b/(d*x+c))/(d*f*x+c*f),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 \[ \text {Timed out} \]_______________________________________________________