\[ \int \frac {\left (\frac {3+3 x}{x}\right )^{\frac {e^{e^4 x} (5-x)}{x}} \left (\left (2 x+2 x^2\right ) \log \left (\frac {3+3 x}{x}\right )+e^{e^4 x} \log \left (\frac {3+3 x}{x}\right ) \left (-10+2 x+\left (-10-10 x+e^4 \left (10 x+8 x^2-2 x^3\right )\right ) \log \left (\frac {3+3 x}{x}\right )\right )\right )}{\left (x+x^2\right ) \log \left (\frac {3+3 x}{x}\right )} \, dx \]
Optimal antiderivative \[ 2 \,{\mathrm e}^{\frac {{\mathrm e}^{x \,{\mathrm e}^{4}+\ln \left (\ln \left (\frac {3}{x}+3\right )\right )} \left (5-x \right )}{x}} x +4 \]
command
integrate(((((-2*x**3+8*x**2+10*x)*exp(4)-10*x-10)*ln((3*x+3)/x)+2*x-10)*exp(ln(ln((3*x+3)/x))+x*exp(4))+(2*x**2+2*x)*ln((3*x+3)/x))*exp((5-x)*exp(ln(ln((3*x+3)/x))+x*exp(4))/x)/(x**2+x)/ln((3*x+3)/x),x)
Sympy 1.10.1 under Python 3.10.4 output
\[ 2 x e^{\frac {\left (5 - x\right ) e^{x e^{4}} \log {\left (\frac {3 x + 3}{x} \right )}}{x}} \]
Sympy 1.8 under Python 3.8.8 output
\[ \text {Timed out} \]________________________________________________________________________________________