\[ \int \frac {-16 e^x x-16 e^x \log (x)+\left (e^x \left (-8-4 x+4 x^2\right )+e^x (4+4 x) \log (x)\right ) \log \left (9 x^2\right )}{\left (x^3+3 x^2 \log (x)+3 x \log ^2(x)+\log ^3(x)\right ) \log ^3\left (9 x^2\right )} \, dx \]
Optimal antiderivative \[ \frac {4 \,{\mathrm e}^{x} x}{\ln \left (9 x^{2}\right )^{2} \left (x +\ln \left (x \right )\right )^{2}}-2 \]
command
int((((4*x+4)*exp(x)*ln(x)+(4*x^2-4*x-8)*exp(x))*ln(9*x^2)-16*exp(x)*ln(x)-16*exp(x)*x)/(ln(x)^3+3*x*ln(x)^2+3*x^2*ln(x)+x^3)/ln(9*x^2)^3,x)
Maple 2022.1 output
\[-\frac {16 x \,{\mathrm e}^{x}}{\left (x +\ln \left (x \right )\right )^{2} \left (\pi \mathrm {csgn}\left (i x^{2}\right )^{3}+\pi \mathrm {csgn}\left (i x \right )^{2} \mathrm {csgn}\left (i x^{2}\right )-2 \pi \,\mathrm {csgn}\left (i x \right ) \mathrm {csgn}\left (i x^{2}\right )^{2}+4 i \ln \left (3\right )+4 i \ln \left (x \right )\right )^{2}}\]
Maple 2021.1 output
\[\int \frac {\left (\left (4 x +4\right ) {\mathrm e}^{x} \ln \left (x \right )+\left (4 x^{2}-4 x -8\right ) {\mathrm e}^{x}\right ) \ln \left (9 x^{2}\right )-16 \,{\mathrm e}^{x} \ln \left (x \right )-16 \,{\mathrm e}^{x} x}{\left (\ln \left (x \right )^{3}+3 x \ln \left (x \right )^{2}+3 x^{2} \ln \left (x \right )+x^{3}\right ) \ln \left (9 x^{2}\right )^{3}}\, dx\]________________________________________________________________________________________