\[ \int \frac {(64-16 x) \log (x)+\left (-64 x+16 x^2\right ) \log (x) \log (2 x)+(64-16 x+(64-48 x) \log (x)) \log (2 x) \log \left (\frac {e^x}{\log (2 x)}\right )}{\left (-64 x^2+48 x^3-12 x^4+x^5\right ) \log ^2(x) \log (2 x)} \, dx \]
Optimal antiderivative \[ \frac {16 \ln \! \left (\frac {{\mathrm e}^{x}}{\ln \left (2 x \right )}\right )}{x \left (4-x \right )^{2} \ln \! \left (x \right )} \]
command
integrate((((-48*x+64)*ln(x)-16*x+64)*ln(2*x)*ln(exp(x)/ln(2*x))+(16*x**2-64*x)*ln(x)*ln(2*x)+(-16*x+64)*ln(x))/(x**5-12*x**4+48*x**3-64*x**2)/ln(x)**2/ln(2*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
\[ \frac {16 \log {\left (\frac {e^{x}}{\log {\left (x \right )} + \log {\left (2 \right )}} \right )}}{x^{3} \log {\left (x \right )} - 8 x^{2} \log {\left (x \right )} + 16 x \log {\left (x \right )}} \]