\[ \int \frac {5-5 e^x+5 x-5 x^2+\left (5+4 x^2+x^3+e^x (-5+6 x)\right ) \log (x)+\left (-x^3+e^x \left (x-x^2\right )\right ) \log ^2(x)+\left (5+(5-x) \log (x)-x \log ^2(x)\right ) \log \left (\frac {1}{2} (-5+x \log (x))\right )}{-5 x^2 \log ^2(x)+x^3 \log ^3(x)} \, dx \]
Optimal antiderivative \[ \frac {x -{\mathrm e}^{x}+1-x^{2}+\ln \! \left (\frac {x \ln \left (x \right )}{2}-\frac {5}{2}\right )}{\ln \! \left (x \right ) x} \]
command
integrate(((-x*ln(x)**2+ln(x)*(5-x)+5)*ln(1/2*x*ln(x)-5/2)+((-x**2+x)*exp(x)-x**3)*ln(x)**2+((6*x-5)*exp(x)+x**3+4*x**2+5)*ln(x)-5*exp(x)-5*x**2+5*x+5)/(x**3*ln(x)**3-5*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
\[ \frac {- x^{2} + x + 1}{x \log {\left (x \right )}} - \frac {e^{x}}{x \log {\left (x \right )}} + \frac {\log {\left (\frac {x \log {\left (x \right )}}{2} - \frac {5}{2} \right )}}{x \log {\left (x \right )}} \]