\[ \int \frac {9-21 x+6 x^2+(3-6 x) \log (4)+(-9+9 x+(-3+3 x) \log (4)) \log \left (-x+x^2\right )+\left (-9+15 x-7 x^2+x^3+\left (-6+8 x-2 x^2\right ) \log (4)+(-1+x) \log ^2(4)\right ) \log ^2\left (-x+x^2\right )}{\left (-9+15 x-7 x^2+x^3+\left (-6+8 x-2 x^2\right ) \log (4)+(-1+x) \log ^2(4)\right ) \log ^2\left (-x+x^2\right )} \, dx \]
Optimal antiderivative \[ \frac {3 x}{\ln \! \left (x^{2}-x \right ) \left (2 \ln \! \left (2\right )+3-x \right )}+x -1 \]
command
Integrate[(9 - 21*x + 6*x^2 + (3 - 6*x)*Log[4] + (-9 + 9*x + (-3 + 3*x)*Log[4])*Log[-x + x^2] + (-9 + 15*x - 7*x^2 + x^3 + (-6 + 8*x - 2*x^2)*Log[4] + (-1 + x)*Log[4]^2)*Log[-x + x^2]^2)/((-9 + 15*x - 7*x^2 + x^3 + (-6 + 8*x - 2*x^2)*Log[4] + (-1 + x)*Log[4]^2)*Log[-x + x^2]^2),x]
Mathematica 13.1 output
\[ \int \frac {9-21 x+6 x^2+(3-6 x) \log (4)+(-9+9 x+(-3+3 x) \log (4)) \log \left (-x+x^2\right )+\left (-9+15 x-7 x^2+x^3+\left (-6+8 x-2 x^2\right ) \log (4)+(-1+x) \log ^2(4)\right ) \log ^2\left (-x+x^2\right )}{\left (-9+15 x-7 x^2+x^3+\left (-6+8 x-2 x^2\right ) \log (4)+(-1+x) \log ^2(4)\right ) \log ^2\left (-x+x^2\right )} \, dx \]
Mathematica 12.3 output
\[ x-\frac {x \left (9-21 x+6 x^2-3 x \log (16)+\log (64)\right )}{(-1+2 x) (-3+x-\log (4))^2 \log ((-1+x) x)} \]