14.110 Problem number 1006

\[ \int \frac {1}{(d+e x)^3 \left (c d^2+2 c d e x+c e^2 x^2\right )} \, dx \]

Optimal antiderivative \[ -\frac {1}{4 c e \left (e x +d \right )^{4}} \]

command

integrate(1/(e*x+d)^3/(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

\[ -\frac {e^{\left (-1\right )}}{4 \, {\left (x e + d\right )}^{4} c} \]

Giac 1.7.0 via sagemath 9.3 output

\[ \text {Exception raised: NotImplementedError} \]________________________________________________________________________________________