\[ \int \frac {(d+e x)^2}{\left (a^2+2 a b x+b^2 x^2\right )^{3/2}} \, dx \]
Optimal antiderivative \[ -\frac {2 e \left (-a e +b d \right )}{b^{3} \sqrt {\left (b x +a \right )^{2}}}-\frac {\left (-a e +b d \right )^{2}}{2 b^{3} \left (b x +a \right ) \sqrt {\left (b x +a \right )^{2}}}+\frac {e^{2} \left (b x +a \right ) \ln \left (b x +a \right )}{b^{3} \sqrt {\left (b x +a \right )^{2}}} \]
command
integrate((e*x+d)^2/(b^2*x^2+2*a*b*x+a^2)^(3/2),x, algorithm="giac")
Giac 1.9.0-11 via sagemath 9.6 output
\[ \frac {e^{2} \log \left ({\left | b x + a \right |}\right )}{b^{3} \mathrm {sgn}\left (b x + a\right )} - \frac {4 \, {\left (b d e - a e^{2}\right )} x + \frac {b^{2} d^{2} + 2 \, a b d e - 3 \, a^{2} e^{2}}{b}}{2 \, {\left (b x + a\right )}^{2} b^{2} \mathrm {sgn}\left (b x + a\right )} \]
Giac 1.7.0 via sagemath 9.3 output
\[ \mathit {sage}_{0} x \]________________________________________________________________________________________