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