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