\[ \int \frac {4 e^5 x^2 \log ^2(x)+e^{\frac {3}{e^5 x^2 \log (x)}} \log \left (2+e^2\right ) \left (6+12 \log (x)-4 e^5 x^2 \log ^2(x)\right )+e^{\frac {6}{e^5 x^2 \log (x)}} \log ^2\left (2+e^2\right ) \left (-3-6 \log (x)+e^5 x^2 \log ^2(x)\right )}{2 e^5 x \log ^2\left (2+e^2\right ) \log ^2(x)} \, dx \]
Optimal antiderivative \[ \left (\frac {x}{\ln \! \left ({\mathrm e}^{2}+2\right )}-\frac {x \,{\mathrm e}^{\frac {3 \,{\mathrm e}^{-5}}{x^{2} \ln \left (x \right )}}}{2}\right )^{2} \]
command
integrate(1/2*((x**2*exp(5)*ln(x)**2-6*ln(x)-3)*ln(exp(2)+2)**2*exp(3/x**2/exp(5)/ln(x))**2+(-4*x**2*exp(5)*ln(x)**2+12*ln(x)+6)*ln(exp(2)+2)*exp(3/x**2/exp(5)/ln(x))+4*x**2*exp(5)*ln(x)**2)/x/exp(5)/ln(x)**2/ln(exp(2)+2)**2,x)
Sympy 1.10.1 under Python 3.10.4 output
\[ \text {Exception raised: TypeError} \]
Sympy 1.8 under Python 3.8.8 output
\[ \frac {x^{2}}{\log {\left (2 + e^{2} \right )}^{2}} + \frac {x^{2} e^{\frac {6}{x^{2} e^{5} \log {\left (x \right )}}} \log {\left (2 + e^{2} \right )} - 4 x^{2} e^{\frac {3}{x^{2} e^{5} \log {\left (x \right )}}}}{4 \log {\left (2 + e^{2} \right )}} \]