\[ \int \frac {x^{-\frac {25}{-84+8 x+x^2+e^{-4-2 x+2 x^2} x^2+e^{-2-x+x^2} x (8+2 x)}} \left (2100-200 x-25 x^2+\left (200 x+50 x^2\right ) \log (x)+e^{-4-2 x+2 x^2} x^2 \left (-25+\left (50-50 x+100 x^2\right ) \log (x)\right )+e^{-2-x+x^2} x \left (-200-50 x+\left (200-100 x+350 x^2+100 x^3\right ) \log (x)\right )\right )}{7056 x-1344 x^2-104 x^3+16 x^4+x^5+e^{-8-4 x+4 x^2} x^5+e^{-6-3 x+3 x^2} x^3 \left (16 x+4 x^2\right )+e^{-4-2 x+2 x^2} x^2 \left (-104 x+48 x^2+6 x^3\right )+e^{-2-x+x^2} x \left (-1344 x-208 x^2+48 x^3+4 x^4\right )} \, dx \]
Optimal antiderivative \[ {\mathrm e}^{\frac {\ln \left (x \right )}{4-\frac {\left ({\mathrm e}^{\ln \left (x \right )+x^{2}-x -2}+4+x \right ) \left (\frac {{\mathrm e}^{\ln \left (x \right )+x^{2}-x -2}}{5}+\frac {4}{5}+\frac {x}{5}\right )}{5}}} \]
command
integrate((((100*x^2-50*x+50)*log(x)-25)*exp(log(x)+x^2-x-2)^2+((100*x^3+350*x^2-100*x+200)*log(x)-50*x-200)*exp(log(x)+x^2-x-2)+(50*x^2+200*x)*log(x)-25*x^2-200*x+2100)*exp(-25*log(x)/(exp(log(x)+x^2-x-2)^2+(2*x+8)*exp(log(x)+x^2-x-2)+x^2+8*x-84))/(x*exp(log(x)+x^2-x-2)^4+(4*x^2+16*x)*exp(log(x)+x^2-x-2)^3+(6*x^3+48*x^2-104*x)*exp(log(x)+x^2-x-2)^2+(4*x^4+48*x^3-208*x^2-1344*x)*exp(log(x)+x^2-x-2)+x^5+16*x^4-104*x^3-1344*x^2+7056*x),x, algorithm="giac")
Giac 1.9.0-11 via sagemath 9.6 output
\[ \frac {1}{x^{\frac {25}{x^{2} e^{\left (2 \, x^{2} - 2 \, x - 4\right )} + 2 \, x^{2} e^{\left (x^{2} - x - 2\right )} + x^{2} + 8 \, x e^{\left (x^{2} - x - 2\right )} + 8 \, x - 84}}} \]
Giac 1.7.0 via sagemath 9.3 output
\[ \text {Timed out} \]________________________________________________________________________________________