\[ \int \frac {\left (\left (-320-16 x-1280 x^2-64 x^3\right ) \log \left (\frac {20+x}{4}\right )+\left (1280 x^2+64 x^3\right ) \log \left (x^2\right ) \log \left (\frac {20+x}{4}\right )\right ) \log \left (\frac {16+64 x^2}{\log \left (x^2\right )}\right )+\left (-4 x-16 x^3\right ) \log \left (x^2\right ) \log ^2\left (\frac {16+64 x^2}{\log \left (x^2\right )}\right )}{\left (20 x+x^2+80 x^3+4 x^4\right ) \log \left (x^2\right ) \log ^2\left (\frac {20+x}{4}\right )} \, dx \]
Optimal antiderivative \[ \frac {4 \ln \! \left (\frac {64 x^{2}+16}{\ln \left (x^{2}\right )}\right )^{2}}{\ln \! \left (5+\frac {x}{4}\right )} \]
command
integrate(((-16*x**3-4*x)*ln(x**2)*ln((64*x**2+16)/ln(x**2))**2+((64*x**3+1280*x**2)*ln(5+1/4*x)*ln(x**2)+(-64*x**3-1280*x**2-16*x-320)*ln(5+1/4*x))*ln((64*x**2+16)/ln(x**2)))/(4*x**4+80*x**3+x**2+20*x)/ln(5+1/4*x)**2/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
\[ \frac {4 \log {\left (\frac {64 x^{2} + 16}{\log {\left (x^{2} \right )}} \right )}^{2}}{\log {\left (\frac {x}{4} + 5 \right )}} \]