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