\[ \int \frac {-8 x^7+4 x^8+6 x^9-5 x^{10}+x^{11}+e^{\frac {256+32 x+x^2}{4 x^6-4 x^7+x^8}} \left (-8 x^7+12 x^8-6 x^9+x^{10}\right )+e^{\frac {256+32 x+x^2}{4 x^6-4 x^7+x^8}} \left (3072+1344 x-1944 x^2-222 x^3-6 x^4\right ) \log (1+x)}{-8 x^7+4 x^8+6 x^9-5 x^{10}+x^{11}} \, dx \]
Optimal antiderivative \[ \ln \! \left (1+x \right ) {\mathrm e}^{\frac {\left (x +16\right )^{2}}{x^{6} \left (2-x \right )^{2}}}+x -5 \]
command
Int[(-8*x^7 + 4*x^8 + 6*x^9 - 5*x^10 + x^11 + E^((256 + 32*x + x^2)/(4*x^6 - 4*x^7 + x^8))*(-8*x^7 + 12*x^8 - 6*x^9 + x^10) + E^((256 + 32*x + x^2)/(4*x^6 - 4*x^7 + x^8))*(3072 + 1344*x - 1944*x^2 - 222*x^3 - 6*x^4)*Log[1 + x])/(-8*x^7 + 4*x^8 + 6*x^9 - 5*x^10 + x^11),x]
Rubi 4.17.3 under Mathematica 13.3.1 output
\[ \int \frac {-8 x^7+4 x^8+6 x^9-5 x^{10}+x^{11}+e^{\frac {256+32 x+x^2}{4 x^6-4 x^7+x^8}} \left (-8 x^7+12 x^8-6 x^9+x^{10}\right )+e^{\frac {256+32 x+x^2}{4 x^6-4 x^7+x^8}} \left (3072+1344 x-1944 x^2-222 x^3-6 x^4\right ) \log (1+x)}{-8 x^7+4 x^8+6 x^9-5 x^{10}+x^{11}} \, dx \]
Rubi 4.16.1 under Mathematica 13.3.1 output
\[ x-\frac {3 e^{\frac {(x+16)^2}{(2-x)^2 x^6}} \left (x^4 (-\log (x+1))-37 x^3 \log (x+1)-324 x^2 \log (x+1)+224 x \log (x+1)+512 \log (x+1)\right )}{(2-x)^3 x^7 (x+1) \left (-\frac {3 (x+16)^2}{(2-x)^2 x^7}+\frac {(x+16)^2}{(2-x)^3 x^6}+\frac {x+16}{(2-x)^2 x^6}\right )} \]