\[ \int \frac {\left (4-4 x^2\right ) \log (5)+\left (-1+x^2\right ) \log ^2(5) \log (-1+x)+\left (\left (-4+4 x^2+e^7 \left (-4-4 x+8 x^2\right )\right ) \log (5)+e^7 \left (-x-x^2\right ) \log ^2(5)+\left (1-x^2+e^7 \left (1+x-2 x^2\right )\right ) \log ^2(5) \log (-1+x)\right ) \log (x)+\left (\left (-4-4 x+8 x^2\right ) \log (5)+\left (-x-x^2\right ) \log ^2(5)+\left (1+x-2 x^2\right ) \log ^2(5) \log (-1+x)\right ) \log (x) \log \left (\frac {\log (x)}{x}\right )}{\left (-16 x^2-16 x^3+16 x^4+16 x^5+\left (8 x^2+8 x^3-8 x^4-8 x^5\right ) \log (5) \log (-1+x)+\left (-x^2-x^3+x^4+x^5\right ) \log ^2(5) \log ^2(-1+x)\right ) \log (x)} \, dx \]
Optimal antiderivative \[ \frac {{\mathrm e}^{7}+\ln \! \left (\frac {\ln \left (x \right )}{x}\right )}{\left (x^{2}+x \right ) \left (\ln \! \left (-1+x \right )-\frac {4}{\ln \left (5\right )}\right )} \]
command
integrate((((-2*x**2+x+1)*ln(5)**2*ln(-1+x)+(-x**2-x)*ln(5)**2+(8*x**2-4*x-4)*ln(5))*ln(x)*ln(ln(x)/x)+(((-2*x**2+x+1)*exp(7)-x**2+1)*ln(5)**2*ln(-1+x)+(-x**2-x)*exp(7)*ln(5)**2+((8*x**2-4*x-4)*exp(7)+4*x**2-4)*ln(5))*ln(x)+(x**2-1)*ln(5)**2*ln(-1+x)+(-4*x**2+4)*ln(5))/((x**5+x**4-x**3-x**2)*ln(5)**2*ln(-1+x)**2+(-8*x**5-8*x**4+8*x**3+8*x**2)*ln(5)*ln(-1+x)+16*x**5+16*x**4-16*x**3-16*x**2)/ln(x),x)
Sympy 1.10.1 under Python 3.10.4 output
\[ \text {Exception raised: TypeError} \]
Sympy 1.8 under Python 3.8.8 output
\[ \frac {\log {\left (5 \right )} \log {\left (\frac {\log {\left (x \right )}}{x} \right )}}{x^{2} \log {\left (5 \right )} \log {\left (x - 1 \right )} - 4 x^{2} + x \log {\left (5 \right )} \log {\left (x - 1 \right )} - 4 x} + \frac {e^{7} \log {\left (5 \right )}}{- 4 x^{2} - 4 x + \left (x^{2} \log {\left (5 \right )} + x \log {\left (5 \right )}\right ) \log {\left (x - 1 \right )}} \]