\[ \int \frac {\left (-128 x^3+256 x^4+\left (128 x^2-256 x^3\right ) \log (2)+\left (-128 x^2+256 x^3+\left (128 x-256 x^2\right ) \log (2)\right ) \log (x)\right ) \log \left (-12-x+x^2\right )+\left (768 x+64 x^2-64 x^3+\left (-768-832 x+64 x^3\right ) \log (2)+\left (-768 x-64 x^2+64 x^3\right ) \log (x)\right ) \log ^2\left (-12-x+x^2\right )}{-12 x^3-x^4+x^5+\left (-24 x^2-2 x^3+2 x^4\right ) \log (x)+\left (-12 x-x^2+x^3\right ) \log ^2(x)} \, dx \]
Optimal antiderivative \[ \frac {64 \ln \! \left (\left (3+x \right ) \left (-4+x \right )\right )^{2} \left (x -\ln \! \left (2\right )\right )}{x +\ln \! \left (x \right )} \]
command
integrate((((64*x**3-64*x**2-768*x)*ln(x)+(64*x**3-832*x-768)*ln(2)-64*x**3+64*x**2+768*x)*ln(x**2-x-12)**2+(((-256*x**2+128*x)*ln(2)+256*x**3-128*x**2)*ln(x)+(-256*x**3+128*x**2)*ln(2)+256*x**4-128*x**3)*ln(x**2-x-12))/((x**3-x**2-12*x)*ln(x)**2+(2*x**4-2*x**3-24*x**2)*ln(x)+x**5-x**4-12*x**3),x)
Sympy 1.10.1 under Python 3.10.4 output
\[ \text {Exception raised: TypeError} \]
Sympy 1.8 under Python 3.8.8 output
\[ \frac {\left (64 x - 64 \log {\left (2 \right )}\right ) \log {\left (x^{2} - x - 12 \right )}^{2}}{x + \log {\left (x \right )}} \]