\[ \int \frac {\frac {1}{27} e^{3 x} x^2+\frac {1}{3} e^{2 x} x^3+e^x x^4+x^5+e^{x+\frac {100}{\frac {e^{2 x}}{9}+\frac {2 e^x x}{3}+x^2}} \left (\frac {1}{27} e^{3 x} (1-x)+200 x+x^3-x^4+\frac {1}{9} e^{2 x} \left (3 x-3 x^2\right )+\frac {1}{3} e^x \left (200 x+3 x^2-3 x^3\right )\right )}{\frac {1}{27} e^{3 x} x^2+\frac {1}{3} e^{2 x} x^3+e^x x^4+x^5} \, dx \]
Optimal antiderivative \[ x -\frac {{\mathrm e}^{x} {\mathrm e}^{\frac {25}{\left (\frac {{\mathrm e}^{-\ln \left (3\right )+x}}{2}+\frac {x}{2}\right )^{2}}}}{x} \]
command
integrate((((1-x)*exp(-log(3)+x)^3+(-3*x^2+3*x)*exp(-log(3)+x)^2+(-3*x^3+3*x^2+200*x)*exp(-log(3)+x)-x^4+x^3+200*x)*exp(x)*exp(100/(exp(-log(3)+x)^2+2*x*exp(-log(3)+x)+x^2))+x^2*exp(-log(3)+x)^3+3*x^3*exp(-log(3)+x)^2+3*x^4*exp(-log(3)+x)+x^5)/(x^2*exp(-log(3)+x)^3+3*x^3*exp(-log(3)+x)^2+3*x^4*exp(-log(3)+x)+x^5),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
\[ \frac {x^{2} - e^{\left (\frac {9 \, x^{3} + 6 \, x^{2} e^{x} + x e^{\left (2 \, x\right )} + 900}{9 \, x^{2} + 6 \, x e^{x} + e^{\left (2 \, x\right )}}\right )}}{x} \]