\[ \int \frac {x-21 x^2+20 x^3+e^5 \left (-20 x+20 x^2\right )+x \log (4 x)+\left (-2 x+2 x^2+e^5 (-2+2 x)+\left (-e^5-x\right ) \log (4 x)\right ) \log \left (e^5+x\right )}{20 x^3-40 x^4+20 x^5+e^5 \left (20 x^2-40 x^3+20 x^4\right )+\left (40 x^3-40 x^4+e^5 \left (40 x^2-40 x^3\right )\right ) \log (4 x)+\left (20 e^5 x^2+20 x^3\right ) \log ^2(4 x)} \, dx \]
Optimal antiderivative \[ \frac {1+\frac {\ln \left ({\mathrm e}^{5}+x \right )}{20 x}}{1+\ln \! \left (4 x \right )-x} \]
command
integrate((((-exp(5)-x)*ln(4*x)+(-2+2*x)*exp(5)+2*x**2-2*x)*ln(exp(5)+x)+x*ln(4*x)+(20*x**2-20*x)*exp(5)+20*x**3-21*x**2+x)/((20*x**2*exp(5)+20*x**3)*ln(4*x)**2+((-40*x**3+40*x**2)*exp(5)-40*x**4+40*x**3)*ln(4*x)+(20*x**4-40*x**3+20*x**2)*exp(5)+20*x**5-40*x**4+20*x**3),x)
Sympy 1.10.1 under Python 3.10.4 output
\[ \text {Exception raised: TypeError} \]
Sympy 1.8 under Python 3.8.8 output
\[ - \frac {\log {\left (x + e^{5} \right )}}{20 x^{2} - 20 x \log {\left (4 x \right )} - 20 x} + \frac {1}{- x + \log {\left (4 x \right )} + 1} \]