\[ \int \frac {\left (-12 x^7+4 x^9+\left (12 x^6-8 x^8\right ) \log (4)\right ) \log ^3\left (\frac {5 x-5 \log (4)}{x^2}\right )+\left (-8 x^9+8 x^8 \log (4)\right ) \log ^4\left (\frac {5 x-5 \log (4)}{x^2}\right )+\log ^3(x) \left (-324 x+108 x^3+\left (324-216 x^2\right ) \log (4)+\left (-216 x^3+216 x^2 \log (4)\right ) \log \left (\frac {5 x-5 \log (4)}{x^2}\right )\right )+\log ^2(x) \left (\left (-324 x^3+108 x^5+\left (324 x^2-216 x^4\right ) \log (4)\right ) \log \left (\frac {5 x-5 \log (4)}{x^2}\right )+\left (-216 x^5+216 x^4 \log (4)\right ) \log ^2\left (\frac {5 x-5 \log (4)}{x^2}\right )\right )+\log (x) \left (\left (-108 x^5+36 x^7+\left (108 x^4-72 x^6\right ) \log (4)\right ) \log ^2\left (\frac {5 x-5 \log (4)}{x^2}\right )+\left (-72 x^7+72 x^6 \log (4)\right ) \log ^3\left (\frac {5 x-5 \log (4)}{x^2}\right )\right )}{-81 x^2+81 x \log (4)} \, dx \]
Optimal antiderivative \[ \left (\ln \left (x \right )+\frac {\ln \left (\frac {5}{x}-\frac {10 \ln \left (2\right )}{x^{2}}\right ) x^{2}}{3}\right )^{4} \]
command
integrate((((432*x**2*ln(2)-216*x**3)*ln((-10*ln(2)+5*x)/x**2)+2*(-216*x**2+324)*ln(2)+108*x**3-324*x)*ln(x)**3+((432*x**4*ln(2)-216*x**5)*ln((-10*ln(2)+5*x)/x**2)**2+(2*(-216*x**4+324*x**2)*ln(2)+108*x**5-324*x**3)*ln((-10*ln(2)+5*x)/x**2))*ln(x)**2+((144*x**6*ln(2)-72*x**7)*ln((-10*ln(2)+5*x)/x**2)**3+(2*(-72*x**6+108*x**4)*ln(2)+36*x**7-108*x**5)*ln((-10*ln(2)+5*x)/x**2)**2)*ln(x)+(16*x**8*ln(2)-8*x**9)*ln((-10*ln(2)+5*x)/x**2)**4+(2*(-8*x**8+12*x**6)*ln(2)+4*x**9-12*x**7)*ln((-10*ln(2)+5*x)/x**2)**3)/(162*x*ln(2)-81*x**2),x)
Sympy 1.10.1 under Python 3.10.4 output
\[ \frac {x^{8} \log {\left (\frac {5 x - 10 \log {\left (2 \right )}}{x^{2}} \right )}^{4}}{81} + \frac {4 x^{6} \log {\left (x \right )} \log {\left (\frac {5 x - 10 \log {\left (2 \right )}}{x^{2}} \right )}^{3}}{27} + \frac {2 x^{4} \log {\left (x \right )}^{2} \log {\left (\frac {5 x - 10 \log {\left (2 \right )}}{x^{2}} \right )}^{2}}{3} + \frac {4 x^{2} \log {\left (x \right )}^{3} \log {\left (\frac {5 x - 10 \log {\left (2 \right )}}{x^{2}} \right )}}{3} + \log {\left (x \right )}^{4} \]
Sympy 1.8 under Python 3.8.8 output
\[ \text {Timed out} \]________________________________________________________________________________________