\[ \int \frac {1}{(d+e x) \left (a d e+\left (c d^2+a e^2\right ) x+c d e x^2\right )} \, dx \]
Optimal antiderivative \[ \frac {1}{\left (-a \,e^{2}+c \,d^{2}\right ) \left (e x +d \right )}+\frac {c d \ln \left (c d x +a e \right )}{\left (-a \,e^{2}+c \,d^{2}\right )^{2}}-\frac {c d \ln \left (e x +d \right )}{\left (-a \,e^{2}+c \,d^{2}\right )^{2}} \]
command
integrate(1/(e*x+d)/(a*d*e+(a*e^2+c*d^2)*x+c*d*e*x^2),x, algorithm="giac")
Giac 1.9.0-11 via sagemath 9.6 output
\[ \frac {c^{2} d^{2} \log \left ({\left | c d x + a e \right |}\right )}{c^{3} d^{5} - 2 \, a c^{2} d^{3} e^{2} + a^{2} c d e^{4}} - \frac {c d e \log \left ({\left | x e + d \right |}\right )}{c^{2} d^{4} e - 2 \, a c d^{2} e^{3} + a^{2} e^{5}} + \frac {1}{{\left (c d^{2} - a e^{2}\right )} {\left (x e + d\right )}} \]
Giac 1.7.0 via sagemath 9.3 output
\[ \text {Exception raised: NotImplementedError} \]________________________________________________________________________________________