\[ \int \frac {(-16-2 x) \log ^2(x)+\left (16 x+2 x^2+2 x^3\right ) \log \left (\frac {8+x}{4}\right )+\log (x) \left (16+2 x+2 x^2+\left (-16 x-2 x^2\right ) \log \left (\frac {8+x}{4}\right )\right )}{8 x^3+x^4} \, dx \]
Optimal antiderivative \[ \left (-\frac {\ln \left (x \right )}{x}-\ln \left (2+\frac {x}{4}\right )\right )^{2} \]
command
integrate(((-2*x-16)*ln(x)**2+((-2*x**2-16*x)*ln(2+1/4*x)+2*x**2+2*x+16)*ln(x)+(2*x**3+2*x**2+16*x)*ln(2+1/4*x))/(x**4+8*x**3),x)
Sympy 1.10.1 under Python 3.10.4 output
\[ \log {\left (\frac {x}{4} + 2 \right )}^{2} + \frac {2 \log {\left (x \right )} \log {\left (\frac {x}{4} + 2 \right )}}{x} + \frac {\log {\left (x \right )}^{2}}{x^{2}} \]
Sympy 1.8 under Python 3.8.8 output
\[ \text {Timed out} \]________________________________________________________________________________________