\[ \int \frac {x^2+2 x \log (x)+\log ^2(x)+e^{\frac {2 \left (25+e x^2+e x \log (x)\right )}{x^2+x \log (x)}} \left (-25-50 x+x^3+\left (-25+2 x^2\right ) \log (x)+x \log ^2(x)\right )}{x^2+2 x \log (x)+\log ^2(x)} \, dx \]
Optimal antiderivative \[ x +\frac {x^{2} {\mathrm e}^{\frac {50}{x \left (x +\ln \left (x \right )\right )}+2 \,{\mathrm e}}}{2}+4 \]
command
integrate(((x*ln(x)**2+(2*x**2-25)*ln(x)+x**3-50*x-25)*exp((x*exp(1)*ln(x)+x**2*exp(1)+25)/(x*ln(x)+x**2))**2+ln(x)**2+2*x*ln(x)+x**2)/(ln(x)**2+2*x*ln(x)+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
\[ \frac {x^{2} e^{\frac {2 \left (e x^{2} + e x \log {\left (x \right )} + 25\right )}{x^{2} + x \log {\left (x \right )}}}}{2} + x \]