\[ \int \frac {12 x-12 x^2-12 x^3+24 x^4-12 x^5+\left (-12+12 x+24 x^2-48 x^3+24 x^4\right ) \log (2)+\left (-12 x+24 x^2-12 x^3\right ) \log ^2(2)+\left (-16+44 x-40 x^2+44 x^3-40 x^4+12 x^5+\left (-16+44 x-88 x^2+80 x^3-24 x^4\right ) \log (2)+\left (-16+44 x-40 x^2+12 x^3\right ) \log ^2(2)\right ) \log \left (\frac {1}{2} (4-3 x)\right )}{\left (-4 x^2+11 x^3-10 x^4+3 x^5+\left (8 x-22 x^2+20 x^3-6 x^4\right ) \log (2)+\left (-4+11 x-10 x^2+3 x^3\right ) \log ^2(2)\right ) \log ^2\left (\frac {1}{2} (4-3 x)\right )} \, dx \]
Optimal antiderivative \[ \frac {4 x -\frac {4 x}{\left (\ln \left (2\right )-x \right ) \left (x^{2}-x \right )}}{\ln \! \left (2-\frac {3 x}{2}\right )} \]
command
Integrate[(12*x - 12*x^2 - 12*x^3 + 24*x^4 - 12*x^5 + (-12 + 12*x + 24*x^2 - 48*x^3 + 24*x^4)*Log[2] + (-12*x + 24*x^2 - 12*x^3)*Log[2]^2 + (-16 + 44*x - 40*x^2 + 44*x^3 - 40*x^4 + 12*x^5 + (-16 + 44*x - 88*x^2 + 80*x^3 - 24*x^4)*Log[2] + (-16 + 44*x - 40*x^2 + 12*x^3)*Log[2]^2)*Log[(4 - 3*x)/2])/((-4*x^2 + 11*x^3 - 10*x^4 + 3*x^5 + (8*x - 22*x^2 + 20*x^3 - 6*x^4)*Log[2] + (-4 + 11*x - 10*x^2 + 3*x^3)*Log[2]^2)*Log[(4 - 3*x)/2]^2),x]
Mathematica 13.1 output
\[ \int \frac {12 x-12 x^2-12 x^3+24 x^4-12 x^5+\left (-12+12 x+24 x^2-48 x^3+24 x^4\right ) \log (2)+\left (-12 x+24 x^2-12 x^3\right ) \log ^2(2)+\left (-16+44 x-40 x^2+44 x^3-40 x^4+12 x^5+\left (-16+44 x-88 x^2+80 x^3-24 x^4\right ) \log (2)+\left (-16+44 x-40 x^2+12 x^3\right ) \log ^2(2)\right ) \log \left (\frac {1}{2} (4-3 x)\right )}{\left (-4 x^2+11 x^3-10 x^4+3 x^5+\left (8 x-22 x^2+20 x^3-6 x^4\right ) \log (2)+\left (-4+11 x-10 x^2+3 x^3\right ) \log ^2(2)\right ) \log ^2\left (\frac {1}{2} (4-3 x)\right )} \, dx \]
Mathematica 12.3 output
\[ \frac {4 \left (3 x^5+x \left (-3+3 \log ^2(2)-\log (8)\right )+\log (8)+3 x^3 \left (1+\log ^2(2)+\log (16)\right )-x^4 (6+\log (64))-x^2 \left (-3+6 \log ^2(2)+\log (64)\right )\right )}{3 (-1+x)^2 (x-\log (2))^2 \log \left (2-\frac {3 x}{2}\right )} \]