\[ \int \frac {8 x-9 \log (2)+(-2 x+2 \log (2)) \log (x)+(x-\log (2)) \log (2 x-2 \log (2))}{-49 x+28 x^2-4 x^3+\left (49-28 x+4 x^2\right ) \log (2)+(-4 x+4 \log (2)) \log ^2(x)+\left (-14 x+4 x^2+(14-4 x) \log (2)\right ) \log (2 x-2 \log (2))+(-x+\log (2)) \log ^2(2 x-2 \log (2))+\log (x) \left (28 x-8 x^2+(-28+8 x) \log (2)+(4 x-4 \log (2)) \log (2 x-2 \log (2))\right )} \, dx \]
Optimal antiderivative \[ -\frac {x}{\ln \! \left (-2 \ln \! \left (2\right )+2 x \right )-2 \ln \! \left (x \right )-2 x +7} \]
command
Integrate[(8*x - 9*Log[2] + (-2*x + 2*Log[2])*Log[x] + (x - Log[2])*Log[2*x - 2*Log[2]])/(-49*x + 28*x^2 - 4*x^3 + (49 - 28*x + 4*x^2)*Log[2] + (-4*x + 4*Log[2])*Log[x]^2 + (-14*x + 4*x^2 + (14 - 4*x)*Log[2])*Log[2*x - 2*Log[2]] + (-x + Log[2])*Log[2*x - 2*Log[2]]^2 + Log[x]*(28*x - 8*x^2 + (-28 + 8*x)*Log[2] + (4*x - 4*Log[2])*Log[2*x - 2*Log[2]])),x]
Mathematica 13.1 output
\[ \int \frac {8 x-9 \log (2)+(-2 x+2 \log (2)) \log (x)+(x-\log (2)) \log (2 x-2 \log (2))}{-49 x+28 x^2-4 x^3+\left (49-28 x+4 x^2\right ) \log (2)+(-4 x+4 \log (2)) \log ^2(x)+\left (-14 x+4 x^2+(14-4 x) \log (2)\right ) \log (2 x-2 \log (2))+(-x+\log (2)) \log ^2(2 x-2 \log (2))+\log (x) \left (28 x-8 x^2+(-28+8 x) \log (2)+(4 x-4 \log (2)) \log (2 x-2 \log (2))\right )} \, dx \]
Mathematica 12.3 output
\[ \frac {x (2 x-\log (4))}{2 (x-\log (2)) (-7+2 x+2 \log (x)-\log (2 x-\log (4)))} \]