\[ \int \frac {\left (1-9 \log \left (\frac {3}{x}\right )\right ) \log (\log (3))+\log \left (\frac {3}{x}\right ) \log (\log (3)) \log \left (\log \left (\frac {3}{x}\right )\right )}{\left (81-72 x+16 x^2\right ) \log \left (\frac {3}{x}\right )+(-18+8 x) \log \left (\frac {3}{x}\right ) \log \left (\log \left (\frac {3}{x}\right )\right )+\log \left (\frac {3}{x}\right ) \log ^2\left (\log \left (\frac {3}{x}\right )\right )} \, dx \]
Optimal antiderivative \[ \ln \left (\ln \left (3\right )\right ) \left (\frac {x}{4 x +\ln \left (\ln \left (\frac {3}{x}\right )\right )-9}+16\right ) \]
command
int((ln(3/x)*ln(ln(3))*ln(ln(3/x))+(-9*ln(3/x)+1)*ln(ln(3)))/(ln(3/x)*ln(ln(3/x))^2+(8*x-18)*ln(3/x)*ln(ln(3/x))+(16*x^2-72*x+81)*ln(3/x)),x,method=_RETURNVERBOSE)
Maple 2022.1 output
| method | result | size |
| default | \(\frac {\ln \left (\ln \left (3\right )\right )}{\frac {\ln \left (\ln \left (3\right )+\ln \left (\frac {1}{x}\right )\right )}{x}-\frac {9}{x}+4}\) | \(26\) |
Maple 2021.1 output
\[\int \frac {\ln \left (\frac {3}{x}\right ) \ln \left (\ln \left (3\right )\right ) \ln \left (\ln \left (\frac {3}{x}\right )\right )+\left (-9 \ln \left (\frac {3}{x}\right )+1\right ) \ln \left (\ln \left (3\right )\right )}{\ln \left (\frac {3}{x}\right ) \ln \left (\ln \left (\frac {3}{x}\right )\right )^{2}+\left (8 x -18\right ) \ln \left (\frac {3}{x}\right ) \ln \left (\ln \left (\frac {3}{x}\right )\right )+\left (16 x^{2}-72 x +81\right ) \ln \left (\frac {3}{x}\right )}\, dx\]________________________________________________________________________________________