\[ \int \frac {(g+h x)^2}{\left (a+b \log \left (c \left (d (e+f x)^p\right )^q\right )\right )^3} \, dx \]
Optimal antiderivative \[ \frac {\left (-e h +f g \right )^{2} \left (f x +e \right ) \expIntegral \left (\frac {a +b \ln \left (c \left (d \left (f x +e \right )^{p}\right )^{q}\right )}{b p q}\right ) {\mathrm e}^{-\frac {a}{b p q}} \left (c \left (d \left (f x +e \right )^{p}\right )^{q}\right )^{-\frac {1}{p q}}}{2 b^{3} f^{3} p^{3} q^{3}}+\frac {4 h \left (-e h +f g \right ) \left (f x +e \right )^{2} \expIntegral \left (\frac {2 a +2 b \ln \left (c \left (d \left (f x +e \right )^{p}\right )^{q}\right )}{b p q}\right ) {\mathrm e}^{-\frac {2 a}{b p q}} \left (c \left (d \left (f x +e \right )^{p}\right )^{q}\right )^{-\frac {2}{p q}}}{b^{3} f^{3} p^{3} q^{3}}+\frac {9 h^{2} \left (f x +e \right )^{3} \expIntegral \left (\frac {3 a +3 b \ln \left (c \left (d \left (f x +e \right )^{p}\right )^{q}\right )}{b p q}\right ) {\mathrm e}^{-\frac {3 a}{b p q}} \left (c \left (d \left (f x +e \right )^{p}\right )^{q}\right )^{-\frac {3}{p q}}}{2 b^{3} f^{3} p^{3} q^{3}}-\frac {\left (f x +e \right ) \left (h x +g \right )^{2}}{2 b f p q \left (a +b \ln \left (c \left (d \left (f x +e \right )^{p}\right )^{q}\right )\right )^{2}}+\frac {\left (-e h +f g \right ) \left (f x +e \right ) \left (h x +g \right )}{b^{2} f^{2} p^{2} q^{2} \left (a +b \ln \left (c \left (d \left (f x +e \right )^{p}\right )^{q}\right )\right )}-\frac {3 \left (f x +e \right ) \left (h x +g \right )^{2}}{2 b^{2} f \,p^{2} q^{2} \left (a +b \ln \left (c \left (d \left (f x +e \right )^{p}\right )^{q}\right )\right )} \]
command
integrate((h*x+g)^2/(a+b*log(c*(d*(f*x+e)^p)^q))^3,x, algorithm="giac")
Giac 1.9.0-11 via sagemath 9.6 output
\[ \text {output too large to display} \]
Giac 1.7.0 via sagemath 9.3 output \[ \text {Timed out} \]_______________________________________________________