\[ \int \frac {e^{\frac {6561+5832 x^2-2916 x^3+1944 x^4-1944 x^5+774 x^6-432 x^7+232 x^8+e^4 x^8+e^5 x^8-68 x^9+24 x^{10}-8 x^{11}+x^{12}+e^2 \left (162 x^4+72 x^6-36 x^7+8 x^8-8 x^9+2 x^{10}\right )+\left (-2916 x^2-1944 x^4+972 x^5-432 x^6+432 x^7-140 x^8+48 x^9-24 x^{10}+4 x^{11}+e^2 \left (-36 x^6-8 x^8+4 x^9\right )\right ) \log (x)+\left (486 x^4+216 x^6-108 x^7+24 x^8+2 e^2 x^8-24 x^9+6 x^{10}\right ) \log ^2(x)+\left (-36 x^6-8 x^8+4 x^9\right ) \log ^3(x)+x^8 \log ^4(x)}{x^8}} \left (-52488-37908 x^2+14580 x^3-9720 x^4+6804 x^5-1980 x^6+864 x^7-140 x^8-20 x^9+24 x^{10}-20 x^{11}+4 x^{12}+e^2 \left (-648 x^4-180 x^6+36 x^7-8 x^8-4 x^9+4 x^{10}\right )+\left (17496 x^2+8748 x^4-2916 x^5+1296 x^6-648 x^7+48 x^8-36 x^{10}+12 x^{11}+e^2 \left (72 x^6+4 x^8+4 x^9\right )\right ) \log (x)+\left (-1944 x^4-540 x^6+108 x^7-24 x^8-12 x^9+12 x^{10}\right ) \log ^2(x)+\left (72 x^6+4 x^8+4 x^9\right ) \log ^3(x)\right )}{x^9} \, dx \]
Optimal antiderivative \[ {\mathrm e}^{\left ({\mathrm e}^{2}+\left (\frac {9}{x^{2}}-\ln \left (x \right )+2-x \right )^{2}\right )^{2}+{\mathrm e}^{5}}-1 \]
command
integrate(((4*x^9+4*x^8+72*x^6)*log(x)^3+(12*x^10-12*x^9-24*x^8+108*x^7-540*x^6-1944*x^4)*log(x)^2+((4*x^9+4*x^8+72*x^6)*exp(2)+12*x^11-36*x^10+48*x^8-648*x^7+1296*x^6-2916*x^5+8748*x^4+17496*x^2)*log(x)+(4*x^10-4*x^9-8*x^8+36*x^7-180*x^6-648*x^4)*exp(2)+4*x^12-20*x^11+24*x^10-20*x^9-140*x^8+864*x^7-1980*x^6+6804*x^5-9720*x^4+14580*x^3-37908*x^2-52488)*exp((x^8*log(x)^4+(4*x^9-8*x^8-36*x^6)*log(x)^3+(2*x^8*exp(2)+6*x^10-24*x^9+24*x^8-108*x^7+216*x^6+486*x^4)*log(x)^2+((4*x^9-8*x^8-36*x^6)*exp(2)+4*x^11-24*x^10+48*x^9-140*x^8+432*x^7-432*x^6+972*x^5-1944*x^4-2916*x^2)*log(x)+x^8*exp(5)+x^8*exp(2)^2+(2*x^10-8*x^9+8*x^8-36*x^7+72*x^6+162*x^4)*exp(2)+x^12-8*x^11+24*x^10-68*x^9+232*x^8-432*x^7+774*x^6-1944*x^5+1944*x^4-2916*x^3+5832*x^2+6561)/x^8)/x^9,x, algorithm="giac")
Giac 1.9.0-11 via sagemath 9.6 output
\[ \text {could not integrate} \]
Giac 1.7.0 via sagemath 9.3 output
\[ e^{\left (x^{4} + 4 \, x^{3} \log \left (x\right ) + 6 \, x^{2} \log \left (x\right )^{2} + 4 \, x \log \left (x\right )^{3} + \log \left (x\right )^{4} - 8 \, x^{3} + 2 \, x^{2} e^{2} - 24 \, x^{2} \log \left (x\right ) + 4 \, x e^{2} \log \left (x\right ) - 24 \, x \log \left (x\right )^{2} + 2 \, e^{2} \log \left (x\right )^{2} - 8 \, \log \left (x\right )^{3} + 24 \, x^{2} - 8 \, x e^{2} + 48 \, x \log \left (x\right ) - 8 \, e^{2} \log \left (x\right ) + 24 \, \log \left (x\right )^{2} - 68 \, x - \frac {108 \, \log \left (x\right )^{2}}{x} - \frac {36 \, \log \left (x\right )^{3}}{x^{2}} - \frac {36 \, e^{2}}{x} + \frac {432 \, \log \left (x\right )}{x} - \frac {36 \, e^{2} \log \left (x\right )}{x^{2}} + \frac {216 \, \log \left (x\right )^{2}}{x^{2}} - \frac {432}{x} + \frac {72 \, e^{2}}{x^{2}} - \frac {432 \, \log \left (x\right )}{x^{2}} + \frac {774}{x^{2}} + \frac {972 \, \log \left (x\right )}{x^{3}} + \frac {486 \, \log \left (x\right )^{2}}{x^{4}} - \frac {1944}{x^{3}} + \frac {162 \, e^{2}}{x^{4}} - \frac {1944 \, \log \left (x\right )}{x^{4}} + \frac {1944}{x^{4}} - \frac {2916}{x^{5}} - \frac {2916 \, \log \left (x\right )}{x^{6}} + \frac {5832}{x^{6}} + \frac {6561}{x^{8}} + e^{5} + e^{4} + 8 \, e^{2} - 140 \, \log \left (x\right ) + 232\right )} \]