\[ \int \frac {\left (-8 x+12 x^2+72 x^3+32 x^4\right ) \log (x)+\left (64-216 x-148 x^2-44 x^3-16 x^4+\left (224 x+284 x^2+60 x^3+32 x^4\right ) \log (x)\right ) \log \left (8+x+x^2\right )}{\left (8 x+x^2+x^3\right ) \log ^2(x)} \, dx \]
Optimal antiderivative \[ \frac {4 \left (2+x \right ) \ln \! \left (x^{2}+x +8\right ) \left (-1+4 x \right )}{\ln \! \left (x \right )} \]
command
integrate((((32*x**4+60*x**3+284*x**2+224*x)*ln(x)-16*x**4-44*x**3-148*x**2-216*x+64)*ln(x**2+x+8)+(32*x**4+72*x**3+12*x**2-8*x)*ln(x))/(x**3+x**2+8*x)/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
\[ \frac {\left (16 x^{2} + 28 x - 8\right ) \log {\left (x^{2} + x + 8 \right )}}{\log {\left (x \right )}} \]