\[ \int \frac {-5 x^2+e^x \left (5 x-x^2+x^3\right )+\left (5 x^2-5 e^x x^2\right ) \log \left (\frac {x}{3}\right )+\left (-12 x+4 x^2+(60-20 x) \log \left (\frac {x}{3}\right )\right ) \log \left (3 x^2\right )+\left (-15+11 x-x^2-15 \log \left (\frac {x}{3}\right )\right ) \log ^2\left (3 x^2\right )}{e^{2 x} x^2-2 e^x x^3+x^4+\left (6 x^2-2 x^3+e^x \left (-6 x+2 x^2\right )\right ) \log ^2\left (3 x^2\right )+\left (9-6 x+x^2\right ) \log ^4\left (3 x^2\right )} \, dx \]
Optimal antiderivative \[ \frac {5 \ln \left (\frac {x}{3}\right )-x}{{\mathrm e}^{x}-\frac {\ln \left (3 x^{2}\right )^{2} \left (3-x \right )}{x}-x} \]
command
integrate(((-15*log(1/3*x)-x^2+11*x-15)*log(3*x^2)^2+((-20*x+60)*log(1/3*x)+4*x^2-12*x)*log(3*x^2)+(-5*exp(x)*x^2+5*x^2)*log(1/3*x)+(x^3-x^2+5*x)*exp(x)-5*x^2)/((x^2-6*x+9)*log(3*x^2)^4+((2*x^2-6*x)*exp(x)-2*x^3+6*x^2)*log(3*x^2)^2+exp(x)^2*x^2-2*exp(x)*x^3+x^4),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 \[ \text {Timed out} \]_______________________________________________________