\[ \int \frac {-16-27 x-2 x^2+\left (3 x+x^2\right ) \log \left (e^{4 x} x^4\right )+\left (5 x-2 x^2+\left (-4 x-x^2\right ) \log \left (e^{4 x} x^4\right )+\left (-5+2 x+(4+x) \log \left (e^{4 x} x^4\right )\right ) \log \left (-5+2 x+(4+x) \log \left (e^{4 x} x^4\right )\right )\right ) \log \left (x-\log \left (-5+2 x+(4+x) \log \left (e^{4 x} x^4\right )\right )\right )}{\left (5 x-2 x^2+\left (-4 x-x^2\right ) \log \left (e^{4 x} x^4\right )+\left (-5+2 x+(4+x) \log \left (e^{4 x} x^4\right )\right ) \log \left (-5+2 x+(4+x) \log \left (e^{4 x} x^4\right )\right )\right ) \log ^2\left (x-\log \left (-5+2 x+(4+x) \log \left (e^{4 x} x^4\right )\right )\right )} \, dx \]
Optimal antiderivative \[ \frac {x}{\ln \left (-\ln \left (\left (4+x \right ) \ln \left (x^{4} {\mathrm e}^{4 x}\right )+2 x -5\right )+x \right )}-5 \]
command
integrate(((((4+x)*ln(x**4*exp(x)**4)+2*x-5)*ln((4+x)*ln(x**4*exp(x)**4)+2*x-5)+(-x**2-4*x)*ln(x**4*exp(x)**4)-2*x**2+5*x)*ln(-ln((4+x)*ln(x**4*exp(x)**4)+2*x-5)+x)+(x**2+3*x)*ln(x**4*exp(x)**4)-2*x**2-27*x-16)/(((4+x)*ln(x**4*exp(x)**4)+2*x-5)*ln((4+x)*ln(x**4*exp(x)**4)+2*x-5)+(-x**2-4*x)*ln(x**4*exp(x)**4)-2*x**2+5*x)/ln(-ln((4+x)*ln(x**4*exp(x)**4)+2*x-5)+x)**2,x)
Sympy 1.10.1 under Python 3.10.4 output
\[ \frac {x}{\log {\left (x - \log {\left (2 x + \left (x + 4\right ) \log {\left (x^{4} e^{4 x} \right )} - 5 \right )} \right )}} \]
Sympy 1.8 under Python 3.8.8 output
\[ \text {Timed out} \]________________________________________________________________________________________