\[ \int \frac {-10 x-x^2+\left (-75+20 x+17 x^2+2 x^3\right ) \log (3)}{\left (-5 x^2-x^3+\left (-75 x-5 x^2+7 x^3+x^4\right ) \log (3)\right ) \log \left (\frac {-x^2+\left (-15 x+2 x^2+x^3\right ) \log (3)}{5+x}\right ) \log \left (5 \log \left (\frac {-x^2+\left (-15 x+2 x^2+x^3\right ) \log (3)}{5+x}\right )\right )} \, dx \]
Optimal antiderivative \[ \ln \left (\ln \left (5 \ln \left (\ln \left (3\right ) x \left (-3+x \right )-\frac {x^{2}}{5+x}\right )\right )\right ) \]
command
int(((2*x^3+17*x^2+20*x-75)*ln(3)-x^2-10*x)/((x^4+7*x^3-5*x^2-75*x)*ln(3)-x^3-5*x^2)/ln(((x^3+2*x^2-15*x)*ln(3)-x^2)/(5+x))/ln(5*ln(((x^3+2*x^2-15*x)*ln(3)-x^2)/(5+x))),x,method=_RETURNVERBOSE)
Maple 2022.1 output
| method | result | size |
| default | \(\ln \left (\ln \left (5\right )+\ln \left (\ln \left (\frac {x \left (x^{2} \ln \left (3\right )+2 x \ln \left (3\right )-15 \ln \left (3\right )-x \right )}{5+x}\right )\right )\right )\) | \(33\) |
Maple 2021.1 output
\[\int \frac {\left (2 x^{3}+17 x^{2}+20 x -75\right ) \ln \left (3\right )-x^{2}-10 x}{\left (\left (x^{4}+7 x^{3}-5 x^{2}-75 x \right ) \ln \left (3\right )-x^{3}-5 x^{2}\right ) \ln \left (\frac {\left (x^{3}+2 x^{2}-15 x \right ) \ln \left (3\right )-x^{2}}{5+x}\right ) \ln \left (5 \ln \left (\frac {\left (x^{3}+2 x^{2}-15 x \right ) \ln \left (3\right )-x^{2}}{5+x}\right )\right )}\, dx\]________________________________________________________________________________________