\[ \int \frac {-50 x-20 e^4 x-2 e^8 x+\left (-20 x-4 e^4 x\right ) \log (x)-2 x \log ^2(x)+e^{\frac {x^3+x^2 \log (4)}{5+e^4+\log (x)}} \left (25+e^8+14 x^3+e^4 \left (10+3 x^3\right )+\left (9 x^2+2 e^4 x^2\right ) \log (4)+\left (10+2 e^4+3 x^3+2 x^2 \log (4)\right ) \log (x)+\log ^2(x)\right )}{25+10 e^4+e^8+\left (10+2 e^4\right ) \log (x)+\log ^2(x)} \, dx \]
Optimal antiderivative \[ x \left ({\mathrm e}^{\frac {\left (x +2 \ln \left (2\right )\right ) x^{2}}{\ln \left (x \right )+5+{\mathrm e}^{4}}}-x \right ) \]
command
integrate(((ln(x)**2+(4*x**2*ln(2)+2*exp(4)+3*x**3+10)*ln(x)+2*(2*x**2*exp(4)+9*x**2)*ln(2)+exp(4)**2+(3*x**3+10)*exp(4)+14*x**3+25)*exp((2*x**2*ln(2)+x**3)/(ln(x)+5+exp(4)))-2*x*ln(x)**2+(-4*x*exp(4)-20*x)*ln(x)-2*x*exp(4)**2-20*x*exp(4)-50*x)/(ln(x)**2+(2*exp(4)+10)*ln(x)+exp(4)**2+10*exp(4)+25),x)
Sympy 1.10.1 under Python 3.10.4 output
\[ \text {Exception raised: TypeError} \]
Sympy 1.8 under Python 3.8.8 output
\[ - x^{2} + x e^{\frac {x^{3} + 2 x^{2} \log {\left (2 \right )}}{\log {\left (x \right )} + 5 + e^{4}}} \]