\[ \int \frac {-4 x^2+2 x^5-4 x^3 \log (2)+2 x \log ^2(2)+\left (-4 x^2-4 x^5+\left (4+8 x^3\right ) \log (2)-4 x \log ^2(2)\right ) \log \left (\frac {-1-x^3+x \log (2)}{-x^2+\log (2)}\right ) \log \left (\log \left (\frac {-1-x^3+x \log (2)}{-x^2+\log (2)}\right )\right )}{\left (x^3+x^6+\left (-x-2 x^4\right ) \log (2)+x^2 \log ^2(2)\right ) \log \left (\frac {-1-x^3+x \log (2)}{-x^2+\log (2)}\right ) \log \left (\log \left (\frac {-1-x^3+x \log (2)}{-x^2+\log (2)}\right )\right )} \, dx \]
Optimal antiderivative \[ \ln \left (\frac {48 \ln \left (\ln \left (x +\frac {1}{x^{2}-\ln \left (2\right )}\right )\right )^{2}}{x^{4}}\right ) \]
command
int(((-4*x*ln(2)^2+(8*x^3+4)*ln(2)-4*x^5-4*x^2)*ln((x*ln(2)-x^3-1)/(ln(2)-x^2))*ln(ln((x*ln(2)-x^3-1)/(ln(2)-x^2)))+2*x*ln(2)^2-4*x^3*ln(2)+2*x^5-4*x^2)/(x^2*ln(2)^2+(-2*x^4-x)*ln(2)+x^6+x^3)/ln((x*ln(2)-x^3-1)/(ln(2)-x^2))/ln(ln((x*ln(2)-x^3-1)/(ln(2)-x^2))),x,method=_RETURNVERBOSE)
Maple 2022.1 output
| method | result | size |
| default | \(-4 \ln \left (x \right )+2 \ln \left (\ln \left (\ln \left (\frac {x \ln \left (2\right )-x^{3}-1}{\ln \left (2\right )-x^{2}}\right )\right )\right )\) | \(33\) |
Maple 2021.1 output
\[\int \frac {\left (-4 x \ln \left (2\right )^{2}+\left (8 x^{3}+4\right ) \ln \left (2\right )-4 x^{5}-4 x^{2}\right ) \ln \left (\frac {x \ln \left (2\right )-x^{3}-1}{\ln \left (2\right )-x^{2}}\right ) \ln \left (\ln \left (\frac {x \ln \left (2\right )-x^{3}-1}{\ln \left (2\right )-x^{2}}\right )\right )+2 x \ln \left (2\right )^{2}-4 x^{3} \ln \left (2\right )+2 x^{5}-4 x^{2}}{\left (x^{2} \ln \left (2\right )^{2}+\left (-2 x^{4}-x \right ) \ln \left (2\right )+x^{6}+x^{3}\right ) \ln \left (\frac {x \ln \left (2\right )-x^{3}-1}{\ln \left (2\right )-x^{2}}\right ) \ln \left (\ln \left (\frac {x \ln \left (2\right )-x^{3}-1}{\ln \left (2\right )-x^{2}}\right )\right )}\, dx\]________________________________________________________________________________________