\[ \int \frac {e^{\frac {-x^3+\log \left (\frac {x^4}{\log ^2(x)}\right )+x \log \left (\frac {\log (3 x)}{\log (x)}\right )}{-x^2+\log \left (\frac {\log (3 x)}{\log (x)}\right )}} \left (\left (2 x^2+\left (-4 x^2+x^5\right ) \log (x)\right ) \log (3 x)+\left (-\log (x)+\left (1+2 x^2 \log (x)\right ) \log (3 x)\right ) \log \left (\frac {x^4}{\log ^2(x)}\right )+\left (-2+\left (4-2 x^3\right ) \log (x)\right ) \log (3 x) \log \left (\frac {\log (3 x)}{\log (x)}\right )+x \log (x) \log (3 x) \log ^2\left (\frac {\log (3 x)}{\log (x)}\right )\right )}{x^5 \log (x) \log (3 x)-2 x^3 \log (x) \log (3 x) \log \left (\frac {\log (3 x)}{\log (x)}\right )+x \log (x) \log (3 x) \log ^2\left (\frac {\log (3 x)}{\log (x)}\right )} \, dx \]
Optimal antiderivative \[ {\mathrm e}^{x +\frac {\ln \left (\frac {x^{4}}{\ln \left (x \right )^{2}}\right )}{\ln \left (\frac {\ln \left (3 x \right )}{\ln \left (x \right )}\right )-x^{2}}} \]
command
int((x*ln(x)*ln(3*x)*ln(ln(3*x)/ln(x))^2+((-2*x^3+4)*ln(x)-2)*ln(3*x)*ln(ln(3*x)/ln(x))+((2*x^2*ln(x)+1)*ln(3*x)-ln(x))*ln(x^4/ln(x)^2)+((x^5-4*x^2)*ln(x)+2*x^2)*ln(3*x))*exp((x*ln(ln(3*x)/ln(x))+ln(x^4/ln(x)^2)-x^3)/(ln(ln(3*x)/ln(x))-x^2))/(x*ln(x)*ln(3*x)*ln(ln(3*x)/ln(x))^2-2*x^3*ln(x)*ln(3*x)*ln(ln(3*x)/ln(x))+x^5*ln(x)*ln(3*x)),x,method=_RETURNVERBOSE)
Maple 2022.1 output
\[ \text {output too large to display} \]
Maple 2021.1 output \[\int \frac {\left (x \ln \left (x \right ) \ln \left (3 x \right ) \ln \left (\frac {\ln \left (3 x \right )}{\ln \left (x \right )}\right )^{2}+\left (\left (-2 x^{3}+4\right ) \ln \left (x \right )-2\right ) \ln \left (3 x \right ) \ln \left (\frac {\ln \left (3 x \right )}{\ln \left (x \right )}\right )+\left (\left (2 x^{2} \ln \left (x \right )+1\right ) \ln \left (3 x \right )-\ln \left (x \right )\right ) \ln \left (\frac {x^{4}}{\ln \left (x \right )^{2}}\right )+\left (\left (x^{5}-4 x^{2}\right ) \ln \left (x \right )+2 x^{2}\right ) \ln \left (3 x \right )\right ) {\mathrm e}^{\frac {x \ln \left (\frac {\ln \left (3 x \right )}{\ln \left (x \right )}\right )+\ln \left (\frac {x^{4}}{\ln \left (x \right )^{2}}\right )-x^{3}}{\ln \left (\frac {\ln \left (3 x \right )}{\ln \left (x \right )}\right )-x^{2}}}}{x \ln \left (x \right ) \ln \left (3 x \right ) \ln \left (\frac {\ln \left (3 x \right )}{\ln \left (x \right )}\right )^{2}-2 x^{3} \ln \left (x \right ) \ln \left (3 x \right ) \ln \left (\frac {\ln \left (3 x \right )}{\ln \left (x \right )}\right )+x^{5} \ln \left (x \right ) \ln \left (3 x \right )}\, dx\]____________________________________________________________________