\[ \int \frac {96 x^2+24 x^3+3 x^5+\left (32+8 x+x^3\right ) \log (2)+\left (32+16 x+2 x^2-2 x^3\right ) \log (2) \log \left (\frac {16+8 x+x^2-x^3}{x^2}\right )}{\left (-48 x^3-24 x^4-3 x^5+3 x^6+\left (-16 x-8 x^2-x^3+x^4\right ) \log (2)\right ) \log \left (\frac {16+8 x+x^2-x^3}{x^2}\right )} \, dx \]
Optimal antiderivative \[ \ln \! \left (\ln \! \left (\left (\frac {4}{x}+1\right )^{2}-x \right )\right )+\ln \! \left (\frac {\ln \! \left (2\right )}{x^{2}}+3\right ) \]
command
Int[(96*x^2 + 24*x^3 + 3*x^5 + (32 + 8*x + x^3)*Log[2] + (32 + 16*x + 2*x^2 - 2*x^3)*Log[2]*Log[(16 + 8*x + x^2 - x^3)/x^2])/((-48*x^3 - 24*x^4 - 3*x^5 + 3*x^6 + (-16*x - 8*x^2 - x^3 + x^4)*Log[2])*Log[(16 + 8*x + x^2 - x^3)/x^2]),x]
Rubi 4.17.3 under Mathematica 13.3.1 output
\[ \int \frac {96 x^2+24 x^3+3 x^5+\left (32+8 x+x^3\right ) \log (2)+\left (32+16 x+2 x^2-2 x^3\right ) \log (2) \log \left (\frac {16+8 x+x^2-x^3}{x^2}\right )}{\left (-48 x^3-24 x^4-3 x^5+3 x^6+\left (-16 x-8 x^2-x^3+x^4\right ) \log (2)\right ) \log \left (\frac {16+8 x+x^2-x^3}{x^2}\right )} \, dx \]
Rubi 4.16.1 under Mathematica 13.3.1 output
\[ \frac {\log (4) \log \left (3 x^2+\log (2)\right )}{2 \log (2)}+\log \left (\log \left (\frac {16}{x^2}-x+\frac {8}{x}+1\right )\right )-\frac {\log (4) \log (x)}{\log (2)} \]