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