\[ \int \frac {e^4 \left (4 x^4-4 x^5+x^6\right )+e^{\frac {2 x^2}{e^4 (-2+x)}} \left (-512 x^3+128 x^4+e^4 \left (-512+384 x^2-128 x^3\right )\right )+\left (e^{\frac {2 x^2}{e^4 (-2+x)}} \left (-512 x^2+128 x^3\right )+e^4 \left (12 x^3-12 x^4+3 x^5\right )\right ) \log (x)+e^4 \left (12 x^2-12 x^3+3 x^4\right ) \log ^2(x)+e^4 \left (4 x-4 x^2+x^3\right ) \log ^3(x)}{e^4 \left (4 x^4-4 x^5+x^6\right )+e^4 \left (12 x^3-12 x^4+3 x^5\right ) \log (x)+e^4 \left (12 x^2-12 x^3+3 x^4\right ) \log ^2(x)+e^4 \left (4 x-4 x^2+x^3\right ) \log ^3(x)} \, dx \]
Optimal antiderivative \[ \frac {64 \,{\mathrm e}^{\frac {2 x^{2} {\mathrm e}^{-4}}{-2+x}}}{\left (x +\ln \! \left (x \right )\right )^{2}}-3+x \]
command
Int[(E^4*(4*x^4 - 4*x^5 + x^6) + E^((2*x^2)/(E^4*(-2 + x)))*(-512*x^3 + 128*x^4 + E^4*(-512 + 384*x^2 - 128*x^3)) + (E^((2*x^2)/(E^4*(-2 + x)))*(-512*x^2 + 128*x^3) + E^4*(12*x^3 - 12*x^4 + 3*x^5))*Log[x] + E^4*(12*x^2 - 12*x^3 + 3*x^4)*Log[x]^2 + E^4*(4*x - 4*x^2 + x^3)*Log[x]^3)/(E^4*(4*x^4 - 4*x^5 + x^6) + E^4*(12*x^3 - 12*x^4 + 3*x^5)*Log[x] + E^4*(12*x^2 - 12*x^3 + 3*x^4)*Log[x]^2 + E^4*(4*x - 4*x^2 + x^3)*Log[x]^3),x]
Rubi 4.17.3 under Mathematica 13.3.1 output
\[ \int \frac {e^4 \left (4 x^4-4 x^5+x^6\right )+e^{\frac {2 x^2}{e^4 (-2+x)}} \left (-512 x^3+128 x^4+e^4 \left (-512+384 x^2-128 x^3\right )\right )+\left (e^{\frac {2 x^2}{e^4 (-2+x)}} \left (-512 x^2+128 x^3\right )+e^4 \left (12 x^3-12 x^4+3 x^5\right )\right ) \log (x)+e^4 \left (12 x^2-12 x^3+3 x^4\right ) \log ^2(x)+e^4 \left (4 x-4 x^2+x^3\right ) \log ^3(x)}{e^4 \left (4 x^4-4 x^5+x^6\right )+e^4 \left (12 x^3-12 x^4+3 x^5\right ) \log (x)+e^4 \left (12 x^2-12 x^3+3 x^4\right ) \log ^2(x)+e^4 \left (4 x-4 x^2+x^3\right ) \log ^3(x)} \, dx \]
Rubi 4.16.1 under Mathematica 13.3.1 output
\[ \frac {64 e^{-\frac {2 x^2}{e^4 (2-x)}-4} \left ((4-x) x^3+(4-x) x^2 \log (x)\right )}{(2-x)^2 \left (\frac {x^2}{e^4 (2-x)^2}+\frac {2 x}{e^4 (2-x)}\right ) x (x+\log (x))^3}+x \]