\[ \int \frac {7040+4096 x+810 x^2+67 x^3+2 x^4+e^9 (7+2 x)+e^6 \left (210+81 x+6 x^2\right )+e^3 \left (2104+1020 x+141 x^2+6 x^3\right )}{1000+e^9+300 x+30 x^2+x^3+e^6 (30+3 x)+e^3 \left (300+60 x+3 x^2\right )} \, dx \]
Optimal antiderivative \[ \left (7+\frac {4}{\left (10+{\mathrm e}^{3}+x \right )^{2}}+x \right ) x \]
command
integrate(((2*x+7)*exp(3)^3+(6*x^2+81*x+210)*exp(3)^2+(6*x^3+141*x^2+1020*x+2104)*exp(3)+2*x^4+67*x^3+810*x^2+4096*x+7040)/(exp(3)^3+(3*x+30)*exp(3)^2+(3*x^2+60*x+300)*exp(3)+x^3+30*x^2+300*x+1000),x, algorithm="giac")
Giac 1.9.0-11 via sagemath 9.6 output
\[ x^{2} + 7 \, x + \frac {4 \, x}{{\left (x + e^{3} + 10\right )}^{2}} \]
Giac 1.7.0 via sagemath 9.3 output
\[ \int \frac {2 \, x^{4} + 67 \, x^{3} + 810 \, x^{2} + {\left (2 \, x + 7\right )} e^{9} + 3 \, {\left (2 \, x^{2} + 27 \, x + 70\right )} e^{6} + {\left (6 \, x^{3} + 141 \, x^{2} + 1020 \, x + 2104\right )} e^{3} + 4096 \, x + 7040}{x^{3} + 30 \, x^{2} + 3 \, {\left (x + 10\right )} e^{6} + 3 \, {\left (x^{2} + 20 \, x + 100\right )} e^{3} + 300 \, x + e^{9} + 1000}\,{d x} \]________________________________________________________________________________________