\[ \int \left (\frac {1}{(c+d x) (-a+c+(-b+d) x) \log \left (\frac {a+b x}{c+d x}\right )}+\frac {\log \left (1-\frac {a+b x}{c+d x}\right )}{(a+b x) (c+d x) \log ^2\left (\frac {a+b x}{c+d x}\right )}\right ) \, dx \]
Optimal antiderivative \[ -\frac {\ln \! \left (1+\frac {-b x -a}{d x +c}\right )}{\left (-a d +b c \right ) \ln \! \left (\frac {b x +a}{d x +c}\right )} \]
command
integrate(1/(d*x+c)/(-a+c+(-b+d)*x)/ln((b*x+a)/(d*x+c))+ln(1+(-b*x-a)/(d*x+c))/(b*x+a)/(d*x+c)/ln((b*x+a)/(d*x+c))**2,x)
Sympy 1.10.1 under Python 3.10.4 output
\[ \text {Exception raised: TypeError} \]
Sympy 1.8 under Python 3.8.8 output
\[ \frac {\log {\left (\frac {- a - b x}{c + d x} + 1 \right )}}{a d \log {\left (\frac {a + b x}{c + d x} \right )} - b c \log {\left (\frac {a + b x}{c + d x} \right )}} \]