\[ \int \frac {1+x}{\log (x) (x+\log (x))} \, dx \]
Optimal antiderivative \[ \logarithmicIntegral \left (x \right )+\ln \left (\ln \left (x \right )\right )-\ln \left (x +\ln \left (x \right )\right ) \]
command
int((1+x)/ln(x)/(x+ln(x)),x,method=_RETURNVERBOSE)
Maple 2022.1 output
| method | result | size |
| default | \(-\expIntegral \left (1, -\ln \left (x \right )\right )+\ln \left (\ln \left (x \right )\right )-\ln \left (x +\ln \left (x \right )\right )\) | \(20\) |
| risch | \(-\expIntegral \left (1, -\ln \left (x \right )\right )+\ln \left (\ln \left (x \right )\right )-\ln \left (x +\ln \left (x \right )\right )\) | \(20\) |
Maple 2021.1 output
\[ \int \frac {x +1}{\left (x +\ln \left (x \right )\right ) \ln \left (x \right )}\, dx \]________________________________________________________________________________________