\[ \int \frac {-720+540 x+3 e^{4+x} x^3+\left (180 x-6 e^{4+x} x^2\right ) \log \left (\frac {x}{\log (5)}\right )+3 e^{4+x} x \log ^2\left (\frac {x}{\log (5)}\right )+\left (-720 x-180 x^2+3 e^{4+x} x^2+\left (720+180 x-6 e^{4+x} x\right ) \log \left (\frac {x}{\log (5)}\right )+3 e^{4+x} \log ^2\left (\frac {x}{\log (5)}\right )\right ) \log \left (\frac {-240-60 x+e^{4+x} x-e^{4+x} \log \left (\frac {x}{\log (5)}\right )}{-x+\log \left (\frac {x}{\log (5)}\right )}\right )}{-240 x-60 x^2+e^{4+x} x^2+\left (240+60 x-2 e^{4+x} x\right ) \log \left (\frac {x}{\log (5)}\right )+e^{4+x} \log ^2\left (\frac {x}{\log (5)}\right )} \, dx \]
Optimal antiderivative \[ 3 \ln \! \left (\frac {60+15 x}{\frac {x}{4}-\frac {\ln \left (\frac {x}{\ln \left (5\right )}\right )}{4}}-{\mathrm e}^{4+x}\right ) x \]
command
integrate(((3*exp(4+x)*ln(x/ln(5))**2+(-6*x*exp(4+x)+180*x+720)*ln(x/ln(5))+3*x**2*exp(4+x)-180*x**2-720*x)*ln((-exp(4+x)*ln(x/ln(5))+x*exp(4+x)-60*x-240)/(ln(x/ln(5))-x))+3*x*exp(4+x)*ln(x/ln(5))**2+(-6*x**2*exp(4+x)+180*x)*ln(x/ln(5))+3*x**3*exp(4+x)+540*x-720)/(exp(4+x)*ln(x/ln(5))**2+(-2*x*exp(4+x)+60*x+240)*ln(x/ln(5))+x**2*exp(4+x)-60*x**2-240*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
\[ 3 x \log {\left (\frac {x e^{x + 4} - 60 x - e^{x + 4} \log {\left (\frac {x}{\log {\left (5 \right )}} \right )} - 240}{- x + \log {\left (\frac {x}{\log {\left (5 \right )}} \right )}} \right )} \]