\[ \int \frac {e^5 \left (-10-2 x+10 x^2+2 x^3\right )+e^{10} \left (10-8 x-2 x^2\right ) \log ^2(5+x)+\log \left (\frac {3 e^x}{x}\right ) \left (e^5 \left (-10 x-2 x^2\right )+4 e^{10} x \log (5+x)\right )}{5 x+11 x^2+7 x^3+x^4+e^5 \left (-10 x-12 x^2-2 x^3\right ) \log ^2(5+x)+e^{10} \left (5 x+x^2\right ) \log ^4(5+x)} \, dx \]
Optimal antiderivative \[ \frac {2 \ln \! \left (\frac {{\mathrm e}^{\ln \left (3\right )+x}}{x}\right )}{\left (1+x \right ) {\mathrm e}^{-5}-\ln \! \left (5+x \right )^{2}} \]
command
integrate(((4*x*exp(5)**2*ln(5+x)+(-2*x**2-10*x)*exp(5))*ln(exp(ln(3)+x)/x)+(-2*x**2-8*x+10)*exp(5)**2*ln(5+x)**2+(2*x**3+10*x**2-2*x-10)*exp(5))/((x**2+5*x)*exp(5)**2*ln(5+x)**4+(-2*x**3-12*x**2-10*x)*exp(5)*ln(5+x)**2+x**4+7*x**3+11*x**2+5*x),x)
Sympy 1.10.1 under Python 3.10.4 output
\[ \text {Exception raised: TypeError} \]
Sympy 1.8 under Python 3.8.8 output
\[ \frac {2 e^{5} \log {\left (\frac {3 e^{x}}{x} \right )}}{x - e^{5} \log {\left (x + 5 \right )}^{2} + 1} \]