\[ \int \frac {4 x^3 \log (x) \log ^2(\log (x))+e^{\frac {-8 x-5 e^3 x+x^2-10 \log (\log (x))}{\log (\log (x))}} \left (8+5 e^3-x+\left (-8-5 e^3+2 x\right ) \log (x) \log (\log (x))\right )+e^{\frac {-8 x-5 e^3 x+x^2-10 \log (\log (x))}{2 \log (\log (x))}} \left (8 x^2+5 e^3 x^2-x^3+\left (-8 x^2-5 e^3 x^2+2 x^3\right ) \log (x) \log (\log (x))+4 x \log (x) \log ^2(\log (x))\right )}{\log (x) \log ^2(\log (x))} \, dx \]
Optimal antiderivative \[ \left (x^{2}+{\mathrm e}^{\frac {x \left (\frac {x}{2}-\frac {5 \,{\mathrm e}^{3}}{2}-4\right )}{\ln \left (\ln \left (x \right )\right )}-5}\right )^{2}+3 \]
command
integrate((((-5*exp(3)+2*x-8)*ln(x)*ln(ln(x))+5*exp(3)+8-x)*exp(1/2*(-10*ln(ln(x))-5*x*exp(3)+x**2-8*x)/ln(ln(x)))**2+(4*x*ln(x)*ln(ln(x))**2+(-5*x**2*exp(3)+2*x**3-8*x**2)*ln(x)*ln(ln(x))+5*x**2*exp(3)-x**3+8*x**2)*exp(1/2*(-10*ln(ln(x))-5*x*exp(3)+x**2-8*x)/ln(ln(x)))+4*x**3*ln(x)*ln(ln(x))**2)/ln(x)/ln(ln(x))**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
\[ x^{4} + 2 x^{2} e^{\frac {\frac {x^{2}}{2} - \frac {5 x e^{3}}{2} - 4 x - 5 \log {\left (\log {\left (x \right )} \right )}}{\log {\left (\log {\left (x \right )} \right )}}} + e^{\frac {2 \left (\frac {x^{2}}{2} - \frac {5 x e^{3}}{2} - 4 x - 5 \log {\left (\log {\left (x \right )} \right )}\right )}{\log {\left (\log {\left (x \right )} \right )}}} \]