\[ \int \frac {6 x^3-4 x^2 \log (2)+e^x \left (-16 x^5+\left (-16 x^3+32 x^4\right ) \log (2)+\left (20 x^2-24 x^3\right ) \log ^2(2)+\left (-8 x+8 x^2\right ) \log ^3(2)+(1-x) \log ^4(2)\right )+e^{2 x} \left (-32 x^5+64 x^4 \log (2)-48 x^3 \log ^2(2)+16 x^2 \log ^3(2)-2 x \log ^4(2)\right )}{x^2+e^x \left (8 x^3-8 x^2 \log (2)+2 x \log ^2(2)\right )+e^{2 x} \left (16 x^4-32 x^3 \log (2)+24 x^2 \log ^2(2)-8 x \log ^3(2)+\log ^4(2)\right )} \, dx \]
Optimal antiderivative \[ \frac {4 x}{4 \,{\mathrm e}^{x}+\frac {4 x}{\left (2 x -\ln \left (2\right )\right )^{2}}}-x^{2} \]
command
Integrate[(6*x^3 - 4*x^2*Log[2] + E^x*(-16*x^5 + (-16*x^3 + 32*x^4)*Log[2] + (20*x^2 - 24*x^3)*Log[2]^2 + (-8*x + 8*x^2)*Log[2]^3 + (1 - x)*Log[2]^4) + E^(2*x)*(-32*x^5 + 64*x^4*Log[2] - 48*x^3*Log[2]^2 + 16*x^2*Log[2]^3 - 2*x*Log[2]^4))/(x^2 + E^x*(8*x^3 - 8*x^2*Log[2] + 2*x*Log[2]^2) + E^(2*x)*(16*x^4 - 32*x^3*Log[2] + 24*x^2*Log[2]^2 - 8*x*Log[2]^3 + Log[2]^4)),x]
Mathematica 13.1 output
\[ \int \frac {6 x^3-4 x^2 \log (2)+e^x \left (-16 x^5+\left (-16 x^3+32 x^4\right ) \log (2)+\left (20 x^2-24 x^3\right ) \log ^2(2)+\left (-8 x+8 x^2\right ) \log ^3(2)+(1-x) \log ^4(2)\right )+e^{2 x} \left (-32 x^5+64 x^4 \log (2)-48 x^3 \log ^2(2)+16 x^2 \log ^3(2)-2 x \log ^4(2)\right )}{x^2+e^x \left (8 x^3-8 x^2 \log (2)+2 x \log ^2(2)\right )+e^{2 x} \left (16 x^4-32 x^3 \log (2)+24 x^2 \log ^2(2)-8 x \log ^3(2)+\log ^4(2)\right )} \, dx \]
Mathematica 12.3 output
\[ x \left (-x+\frac {64 x^7-\log ^6(2)+x \log ^5(2) (8+\log (2))-64 x^6 (-1+\log (8))-x^2 \log ^3(2) \left (4 \log ^2(2)+\log (4)+2 \log (2) (9+\log (16))\right )-16 x^4 \log ^2(2) (-5+\log (1024))+16 x^5 \log (2) (-8+\log (32768))+4 x^3 \log ^3(2) \log (32768)}{(2 x-\log (2))^3 \left (2 x^2-x (-2+\log (2))+\log (2)\right ) \left (x+4 e^x x^2-4 e^x x \log (2)+e^x \log ^2(2)\right )}\right ) \]