\[ \int \frac {2496 x \log (1-2 x)+(240-480 x) \log ^2(1-2 x)+\left (-768 x \log (1-2 x)+(-192+384 x) \log ^2(1-2 x)\right ) \log \left (x^2\right )}{-169 x^2+338 x^3+\left (104 x^2-208 x^3\right ) \log \left (x^2\right )+\left (-16 x^2+32 x^3\right ) \log ^2\left (x^2\right )} \, dx \]
Optimal antiderivative \[ \frac {16 \ln \! \left (1-2 x \right )^{2}}{x \left (\frac {16}{3}-\frac {4 \ln \left (x^{2}\right )}{3}\right )-x} \]
command
integrate((((384*x-192)*ln(1-2*x)**2-768*x*ln(1-2*x))*ln(x**2)+(-480*x+240)*ln(1-2*x)**2+2496*x*ln(1-2*x))/((32*x**3-16*x**2)*ln(x**2)**2+(-208*x**3+104*x**2)*ln(x**2)+338*x**3-169*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
\[ - \frac {48 \log {\left (1 - 2 x \right )}^{2}}{4 x \log {\left (x^{2} \right )} - 13 x} \]