\[ \int \frac {2 e^{\frac {1}{5} (-10-2 \log (x))}}{\left (-20 x+5 e^{\frac {1}{5} (-10-2 \log (x))} x\right ) \log \left (4-e^{\frac {1}{5} (-10-2 \log (x))}\right )} \, dx \]
Optimal antiderivative \[ \ln \left (3\right )-\ln \left (\ln \left (-{\mathrm e}^{-\frac {2 \ln \left (x \right )}{5}-2}+4\right )\right ) \]
command
int(2*exp(-2/5*ln(x)-2)/(5*x*exp(-2/5*ln(x)-2)-20*x)/ln(-exp(-2/5*ln(x)-2)+4),x,method=_RETURNVERBOSE)
Maple 2022.1 output
| method | result | size |
| default | \(-\ln \left (\ln \left (-\frac {{\mathrm e}^{-2}}{x^{\frac {2}{5}}}+4\right )\right )\) | \(14\) |
Maple 2021.1 output
\[\int \frac {2 \,{\mathrm e}^{-\frac {2 \ln \left (x \right )}{5}-2}}{\left (5 x \,{\mathrm e}^{-\frac {2 \ln \left (x \right )}{5}-2}-20 x \right ) \ln \left (-{\mathrm e}^{-\frac {2 \ln \left (x \right )}{5}-2}+4\right )}\, dx\]________________________________________________________________________________________