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