\[ \int \frac {e^x (1-x)+\left (-4 e^{2 x}+e^x x\right ) \log \left (e^{-x} \left (-4 e^x+x\right )\right ) \log \left (\log \left (e^{-x} \left (-4 e^x+x\right )\right )\right )+\left (8 e^{2 x}-2 e^x x\right ) \log \left (e^{-x} \left (-4 e^x+x\right )\right ) \log (\log (\log (16)))}{\left (8 e^x-2 x\right ) \log \left (e^{-x} \left (-4 e^x+x\right )\right )} \, dx \]
Optimal antiderivative \[ \left (\ln \! \left (\ln \! \left (4 \ln \! \left (2\right )\right )\right )-\frac {\ln \! \left (\ln \! \left (x \,{\mathrm e}^{-x}-4\right )\right )}{2}\right ) {\mathrm e}^{x} \]
command
integrate(((-4*exp(x)**2+exp(x)*x)*ln((-4*exp(x)+x)/exp(x))*ln(ln((-4*exp(x)+x)/exp(x)))+(8*exp(x)**2-2*exp(x)*x)*ln((-4*exp(x)+x)/exp(x))*ln(ln(4*ln(2)))+(1-x)*exp(x))/(8*exp(x)-2*x)/ln((-4*exp(x)+x)/exp(x)),x)
Sympy 1.10.1 under Python 3.10.4 output
\[ \text {Timed out} \]
Sympy 1.8 under Python 3.8.8 output
\[ - \frac {e^{x} \log {\left (\log {\left (\left (x - 4 e^{x}\right ) e^{- x} \right )} \right )}}{2} + e^{x} \log {\left (\log {\left (\log {\left (2 \right )} \right )} + 2 \log {\left (2 \right )} \right )} \]