\[ \int \frac {\left (3+12 x^2\right ) \log ^2(x)+e^{\frac {4+4 x \log (x)}{x \log (x)}} \left (-80 x-80 x \log (x)+60 x^2 \log ^2(x)\right )+e^{\frac {2 (4+4 x \log (x))}{x \log (x)}} \left (-200 x-200 x \log (x)+75 x^2 \log ^2(x)\right )}{\log ^2(x)} \, dx \]
Optimal antiderivative \[ x \left (3+\left (2+5 \,{\mathrm e}^{\frac {4 x^{2}+\frac {4 x}{\ln \left (x \right )}}{x^{2}}}\right )^{2} x^{2}\right ) \]
command
integrate(((75*x**2*ln(x)**2-200*x*ln(x)-200*x)*exp((4*x*ln(x)+4)/x/ln(x))**2+(60*x**2*ln(x)**2-80*x*ln(x)-80*x)*exp((4*x*ln(x)+4)/x/ln(x))+(12*x**2+3)*ln(x)**2)/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
\[ 25 x^{3} e^{\frac {2 \left (4 x \log {\left (x \right )} + 4\right )}{x \log {\left (x \right )}}} + 20 x^{3} e^{\frac {4 x \log {\left (x \right )} + 4}{x \log {\left (x \right )}}} + 4 x^{3} + 3 x \]