\[ \int \frac {e^{\frac {20+5 x+x \log (x)+5 \log ^2(x)}{4+x+\log ^2(x)}} \left (-128-56 x-6 x^2+8 x \log (x)+(-64-18 x) \log ^2(x)+2 x \log ^3(x)-8 \log ^4(x)\right )}{16 x^5+8 x^6+x^7+\left (8 x^5+2 x^6\right ) \log ^2(x)+x^5 \log ^4(x)} \, dx \]
Optimal antiderivative \[ \frac {2 \,{\mathrm e}^{\frac {x}{\frac {4+x}{\ln \left (x \right )}+\ln \left (x \right )}+5}}{x^{4}} \]
command
integrate((-8*ln(x)**4+2*x*ln(x)**3+(-18*x-64)*ln(x)**2+8*x*ln(x)-6*x**2-56*x-128)*exp((5*ln(x)**2+x*ln(x)+20+5*x)/(ln(x)**2+4+x))/(x**5*ln(x)**4+(2*x**6+8*x**5)*ln(x)**2+x**7+8*x**6+16*x**5),x)
Sympy 1.10.1 under Python 3.10.4 output
\[ \text {Exception raised: TypeError} \]
Sympy 1.8 under Python 3.8.8 output
\[ \frac {2 e^{\frac {x \log {\left (x \right )} + 5 x + 5 \log {\left (x \right )}^{2} + 20}{x + \log {\left (x \right )}^{2} + 4}}}{x^{4}} \]