\[ \int \frac {\left (486 x-324 x^2-108 x^3+144 x^4-42 x^5+4 x^6+e^x \left (-162 x+216 x^2-108 x^3+24 x^4-2 x^5\right )+\left (324-108 x-216 x^2+168 x^3-44 x^4+4 x^5\right ) \log (x)\right ) \log \left (e^x-x-x^2+\log (5)-2 x \log (x)-\log ^2(x)\right )+\left (-270 x^2+54 x^3+180 x^4-116 x^5+26 x^6-2 x^7+e^x \left (270 x-324 x^2+144 x^3-28 x^4+2 x^5\right )+\left (270 x-324 x^2+144 x^3-28 x^4+2 x^5\right ) \log (5)+\left (-540 x^2+648 x^3-288 x^4+56 x^5-4 x^6\right ) \log (x)+\left (-270 x+324 x^2-144 x^3+28 x^4-2 x^5\right ) \log ^2(x)\right ) \log ^2\left (e^x-x-x^2+\log (5)-2 x \log (x)-\log ^2(x)\right )}{-e^{3 x} x+e^{2 x} \left (x^2+x^3-x \log (5)\right )+2 e^{2 x} x^2 \log (x)+e^{2 x} x \log ^2(x)} \, dx \]
Optimal antiderivative \[ \left (3-x \right )^{4} \ln \! \left ({\mathrm e}^{x}+\ln \! \left (5\right )-\left (x +\ln \! \left (x \right )\right )^{2}-x \right )^{2} {\mathrm e}^{-2 x} \]
command
integrate((((-2*x**5+28*x**4-144*x**3+324*x**2-270*x)*ln(x)**2+(-4*x**6+56*x**5-288*x**4+648*x**3-540*x**2)*ln(x)+(2*x**5-28*x**4+144*x**3-324*x**2+270*x)*exp(x)+(2*x**5-28*x**4+144*x**3-324*x**2+270*x)*ln(5)-2*x**7+26*x**6-116*x**5+180*x**4+54*x**3-270*x**2)*ln(-ln(x)**2-2*x*ln(x)+exp(x)+ln(5)-x**2-x)**2+((4*x**5-44*x**4+168*x**3-216*x**2-108*x+324)*ln(x)+(-2*x**5+24*x**4-108*x**3+216*x**2-162*x)*exp(x)+4*x**6-42*x**5+144*x**4-108*x**3-324*x**2+486*x)*ln(-ln(x)**2-2*x*ln(x)+exp(x)+ln(5)-x**2-x))/(x*exp(x)**2*ln(x)**2+2*x**2*exp(x)**2*ln(x)-x*exp(x)**3+(-x*ln(5)+x**3+x**2)*exp(x)**2),x)
Sympy 1.10.1 under Python 3.10.4 output
\[ \text {Timed out} \]
Sympy 1.8 under Python 3.8.8 output
\[ \left (x^{4} - 12 x^{3} + 54 x^{2} - 108 x + 81\right ) e^{- 2 x} \log {\left (- x^{2} - 2 x \log {\left (x \right )} - x + e^{x} - \log {\left (x \right )}^{2} + \log {\left (5 \right )} \right )}^{2} \]