\[ \int \frac {12-16 x}{\left (-x+x^2\right ) \log \left (\frac {-x^3+x^4}{9 \log (\log (4))}\right )+\left (-2 x+2 x^2\right ) \log \left (\frac {-x^3+x^4}{9 \log (\log (4))}\right ) \log \left (\log \left (\frac {-x^3+x^4}{9 \log (\log (4))}\right )\right )+\left (-x+x^2\right ) \log \left (\frac {-x^3+x^4}{9 \log (\log (4))}\right ) \log ^2\left (\log \left (\frac {-x^3+x^4}{9 \log (\log (4))}\right )\right )} \, dx \]
Optimal antiderivative \[ \frac {4}{1+\ln \left (\ln \left (\frac {x^{2} \left (x^{2}-x \right )}{9 \ln \left (2 \ln \left (2\right )\right )}\right )\right )} \]
command
int((-16*x+12)/((x^2-x)*ln(1/9*(x^4-x^3)/ln(2*ln(2)))*ln(ln(1/9*(x^4-x^3)/ln(2*ln(2))))^2+(2*x^2-2*x)*ln(1/9*(x^4-x^3)/ln(2*ln(2)))*ln(ln(1/9*(x^4-x^3)/ln(2*ln(2))))+(x^2-x)*ln(1/9*(x^4-x^3)/ln(2*ln(2)))),x,method=_RETURNVERBOSE)
Maple 2022.1 output
| method | result | size |
| default | \(\frac {4}{\ln \left (-2 \ln \left (3\right )-\ln \left (\ln \left (2\right )+\ln \left (\ln \left (2\right )\right )\right )+\ln \left (x^{3} \left (x -1\right )\right )\right )+1}\) | \(30\) |
Maple 2021.1 output
\[\int \frac {-16 x +12}{\left (x^{2}-x \right ) \ln \left (\frac {x^{4}-x^{3}}{9 \ln \left (2 \ln \left (2\right )\right )}\right ) \ln \left (\ln \left (\frac {x^{4}-x^{3}}{9 \ln \left (2 \ln \left (2\right )\right )}\right )\right )^{2}+\left (2 x^{2}-2 x \right ) \ln \left (\frac {x^{4}-x^{3}}{9 \ln \left (2 \ln \left (2\right )\right )}\right ) \ln \left (\ln \left (\frac {x^{4}-x^{3}}{9 \ln \left (2 \ln \left (2\right )\right )}\right )\right )+\left (x^{2}-x \right ) \ln \left (\frac {x^{4}-x^{3}}{9 \ln \left (2 \ln \left (2\right )\right )}\right )}\, dx\]________________________________________________________________________________________