\[ \int \frac {-16 x-16 x^2 \log (2)+\left (-20+20 x-4 x^3\right ) \log ^2(2)+\left (16 x \log (2)+8 x^2 \log ^2(2)\right ) \log (-x)-4 x \log ^2(2) \log ^2(-x)}{64 x-32 x^2+4 x^3+\left (-80 x+84 x^2-32 x^3+4 x^4\right ) \log (2)+\left (25 x-40 x^2+26 x^3-8 x^4+x^5\right ) \log ^2(2)+\left (\left (-64 x+32 x^2-4 x^3\right ) \log (2)+\left (40 x-42 x^2+16 x^3-2 x^4\right ) \log ^2(2)\right ) \log (-x)+\left (16 x-8 x^2+x^3\right ) \log ^2(2) \log ^2(-x)} \, dx \]
Optimal antiderivative \[ \frac {4}{\frac {5}{\frac {2}{\ln \left (2\right )}+x -\ln \left (-x \right )}+x -4} \]
command
Integrate[(-16*x - 16*x^2*Log[2] + (-20 + 20*x - 4*x^3)*Log[2]^2 + (16*x*Log[2] + 8*x^2*Log[2]^2)*Log[-x] - 4*x*Log[2]^2*Log[-x]^2)/(64*x - 32*x^2 + 4*x^3 + (-80*x + 84*x^2 - 32*x^3 + 4*x^4)*Log[2] + (25*x - 40*x^2 + 26*x^3 - 8*x^4 + x^5)*Log[2]^2 + ((-64*x + 32*x^2 - 4*x^3)*Log[2] + (40*x - 42*x^2 + 16*x^3 - 2*x^4)*Log[2]^2)*Log[-x] + (16*x - 8*x^2 + x^3)*Log[2]^2*Log[-x]^2),x]
Mathematica 13.1 output
\[ \int \frac {-16 x-16 x^2 \log (2)+\left (-20+20 x-4 x^3\right ) \log ^2(2)+\left (16 x \log (2)+8 x^2 \log ^2(2)\right ) \log (-x)-4 x \log ^2(2) \log ^2(-x)}{64 x-32 x^2+4 x^3+\left (-80 x+84 x^2-32 x^3+4 x^4\right ) \log (2)+\left (25 x-40 x^2+26 x^3-8 x^4+x^5\right ) \log ^2(2)+\left (\left (-64 x+32 x^2-4 x^3\right ) \log (2)+\left (40 x-42 x^2+16 x^3-2 x^4\right ) \log ^2(2)\right ) \log (-x)+\left (16 x-8 x^2+x^3\right ) \log ^2(2) \log ^2(-x)} \, dx \]
Mathematica 12.3 output
\[ -\frac {4 \left (-x^4 \log ^3(2)+x^3 \log (2) \left (5 \log ^2(2)-\log (4)+\log (2) \log (16)\right )+x^2 \left (-15 \log ^3(2)-\log ^2(2) (-2+\log (16))+\log ^2(16)\right )-\log (2) \log (16) \log (32)+\log (16) \log (256)+\log ^2(2) \log (1048576)+x \log (2) \left (-5 \log ^2(2)+\log (4)+\log (2) (-40+\log (2097152))\right )+\left (x^3 \log ^3(2)-x \log (4) \log (16)-\log (2) \log ^2(16)-x^2 \log ^2(2) \log (512)+x \log ^2(2) (8+\log (524288))\right ) \log (-x)\right )}{\left (x^3 \log ^2(2)-\log ^2(16)-x^2 \left (\log ^2(2)+\log (4) \log (16)\right )+x (-\log (2) \log (32)+\log (16) \log (64))\right ) \left (-8+x (2-4 \log (2))+x^2 \log (2)+\log (32)+(-x \log (2)+\log (16)) \log (-x)\right )} \]