\[ \int \frac {\left (-126-447 x-576 x^2-320 x^3-64 x^4\right ) \log \left (\frac {2}{2+x}\right )-2 \log \left (\log \left (\frac {2}{2+x}\right )\right )}{\left (-28-140 x-255 x^2-224 x^3-96 x^4-16 x^5\right ) \log \left (\frac {2}{2+x}\right )+(2+x) \log \left (\frac {2}{2+x}\right ) \log ^2\left (\log \left (\frac {2}{2+x}\right )\right )} \, dx \]
Optimal antiderivative \[ \ln \left (x +2+\ln \left (\ln \left (\frac {2}{2+x}\right )\right )^{2}-\left (2 x +2\right )^{4}\right ) \]
command
int((-2*ln(ln(2/(2+x)))+(-64*x^4-320*x^3-576*x^2-447*x-126)*ln(2/(2+x)))/((2+x)*ln(2/(2+x))*ln(ln(2/(2+x)))^2+(-16*x^5-96*x^4-224*x^3-255*x^2-140*x-28)*ln(2/(2+x))),x,method=_RETURNVERBOSE)
Maple 2022.1 output
| method | result | size |
| default | \(\ln \left (\ln \left (\ln \left (2\right )+\ln \left (\frac {1}{2+x}\right )\right )^{2}-\left (\frac {16}{\left (2+x \right )^{4}}-\frac {65}{\left (2+x \right )^{3}}+\frac {96}{\left (2+x \right )^{2}}-\frac {64}{2+x}+16\right ) \left (2+x \right )^{4}\right )\) | \(52\) |
Maple 2021.1 output
\[\int \frac {-2 \ln \left (\ln \left (\frac {2}{2+x}\right )\right )+\left (-64 x^{4}-320 x^{3}-576 x^{2}-447 x -126\right ) \ln \left (\frac {2}{2+x}\right )}{\left (2+x \right ) \ln \left (\frac {2}{2+x}\right ) \ln \left (\ln \left (\frac {2}{2+x}\right )\right )^{2}+\left (-16 x^{5}-96 x^{4}-224 x^{3}-255 x^{2}-140 x -28\right ) \ln \left (\frac {2}{2+x}\right )}\, dx\]________________________________________________________________________________________