\[ \int \frac {-4+6 x-2 x^2+\left (2 x-x^2+x \log (x)\right ) \log (24-12 x+12 \log (x))+\left (-4+4 x-x^2+(-2+x) \log (x)\right ) \log (24-12 x+12 \log (x)) \log \left (\frac {1}{(-8+4 x) \log ^2(24-12 x+12 \log (x))}\right )}{\left (-20 x^2+20 x^3-5 x^4+\left (-10 x^2+5 x^3\right ) \log (x)\right ) \log (24-12 x+12 \log (x))+\left (-40 x+40 x^2-10 x^3+\left (-20 x+10 x^2\right ) \log (x)\right ) \log (24-12 x+12 \log (x)) \log \left (\frac {1}{(-8+4 x) \log ^2(24-12 x+12 \log (x))}\right )+\left (-20+20 x-5 x^2+(-10+5 x) \log (x)\right ) \log (24-12 x+12 \log (x)) \log ^2\left (\frac {1}{(-8+4 x) \log ^2(24-12 x+12 \log (x))}\right )} \, dx \]
Optimal antiderivative \[ \frac {x}{5 x +5 \ln \left (\frac {1}{4 \ln \left (12 \ln \left (x \right )-12 x +24\right )^{2} \left (-2+x \right )}\right )} \]
command
integrate((((-2+x)*log(x)-x^2+4*x-4)*log(12*log(x)-12*x+24)*log(1/(4*x-8)/log(12*log(x)-12*x+24)^2)+(x*log(x)-x^2+2*x)*log(12*log(x)-12*x+24)-2*x^2+6*x-4)/(((5*x-10)*log(x)-5*x^2+20*x-20)*log(12*log(x)-12*x+24)*log(1/(4*x-8)/log(12*log(x)-12*x+24)^2)^2+((10*x^2-20*x)*log(x)-10*x^3+40*x^2-40*x)*log(12*log(x)-12*x+24)*log(1/(4*x-8)/log(12*log(x)-12*x+24)^2)+((5*x^3-10*x^2)*log(x)-5*x^4+20*x^3-20*x^2)*log(12*log(x)-12*x+24)),x, algorithm="giac")
Giac 1.9.0-11 via sagemath 9.6 output
\[ \text {output too large to display} \]
Giac 1.7.0 via sagemath 9.3 output \[ \text {Timed out} \]_______________________________________________________