\[ \int \frac {\left (5 x+4 e^3 x\right ) \log (x)+\left (-19+e^3 (8-4 x)-5 x\right ) \log \left (\frac {1}{5} \left (38+10 x+e^3 (-16+8 x)\right )\right )}{\left (19 x+5 x^2+e^3 \left (-8 x+4 x^2\right )\right ) \log ^2(x)} \, dx \]
Optimal antiderivative \[ \frac {\ln \! \left (\frac {38}{5}+2 x -\frac {8 \left (2-x \right ) {\mathrm e}^{3}}{5}\right )}{\ln \! \left (x \right )} \]
command
integrate((((-4*x+8)*exp(3)-5*x-19)*ln(1/5*(8*x-16)*exp(3)+2*x+38/5)+(4*x*exp(3)+5*x)*ln(x))/((4*x**2-8*x)*exp(3)+5*x**2+19*x)/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
\[ \frac {\log {\left (2 x + \left (\frac {8 x}{5} - \frac {16}{5}\right ) e^{3} + \frac {38}{5} \right )}}{\log {\left (x \right )}} \]