\[ \int \frac {-7938-11250 e^8-18900 x-11250 x^2+e^4 (18900+22500 x)+e^{-\frac {50 x}{-21+25 e^4-25 x}} \left (-882-1250 e^8-1050 x-1250 x^2+e^4 (2100+1250 x)\right )+e^{-\frac {25 x}{-21+25 e^4-25 x}} \left (-5292-7500 e^8-9450 x-7500 x^2+e^4 (12600+11250 x)\right )}{3969 x^3+5625 e^8 x^3+9450 x^4+5625 x^5+e^4 \left (-9450 x^3-11250 x^4\right )} \, dx \]
Optimal antiderivative \[ \frac {\left ({\mathrm e}^{\frac {x}{\frac {21}{25}+x -{\mathrm e}^{4}}}+3\right )^{2}}{9 x^{2}} \]
command
integrate(((-1250*exp(4)^2+(1250*x+2100)*exp(4)-1250*x^2-1050*x-882)*exp(-25*x/(25*exp(4)-25*x-21))^2+(-7500*exp(4)^2+(11250*x+12600)*exp(4)-7500*x^2-9450*x-5292)*exp(-25*x/(25*exp(4)-25*x-21))-11250*exp(4)^2+(22500*x+18900)*exp(4)-11250*x^2-18900*x-7938)/(5625*x^3*exp(4)^2+(-11250*x^4-9450*x^3)*exp(4)+5625*x^5+9450*x^4+3969*x^3),x, algorithm="giac")
Giac 1.9.0-11 via sagemath 9.6 output
\[ -\frac {\frac {281250 \, x e^{8}}{25 \, x - 25 \, e^{4} + 21} - \frac {472500 \, x e^{4}}{25 \, x - 25 \, e^{4} + 21} + \frac {22050 \, x e^{\left (\frac {50 \, x}{25 \, x - 25 \, e^{4} + 21}\right )}}{25 \, x - 25 \, e^{4} + 21} - \frac {275625 \, x^{2} e^{\left (\frac {50 \, x}{25 \, x - 25 \, e^{4} + 21}\right )}}{{\left (25 \, x - 25 \, e^{4} + 21\right )}^{2}} + \frac {132300 \, x e^{\left (\frac {25 \, x}{25 \, x - 25 \, e^{4} + 21}\right )}}{25 \, x - 25 \, e^{4} + 21} - \frac {1653750 \, x^{2} e^{\left (\frac {25 \, x}{25 \, x - 25 \, e^{4} + 21}\right )}}{{\left (25 \, x - 25 \, e^{4} + 21\right )}^{2}} + \frac {31250 \, x e^{\left (\frac {50 \, x}{25 \, x - 25 \, e^{4} + 21} + 8\right )}}{25 \, x - 25 \, e^{4} + 21} - \frac {390625 \, x^{2} e^{\left (\frac {50 \, x}{25 \, x - 25 \, e^{4} + 21} + 8\right )}}{{\left (25 \, x - 25 \, e^{4} + 21\right )}^{2}} - \frac {52500 \, x e^{\left (\frac {50 \, x}{25 \, x - 25 \, e^{4} + 21} + 4\right )}}{25 \, x - 25 \, e^{4} + 21} + \frac {656250 \, x^{2} e^{\left (\frac {50 \, x}{25 \, x - 25 \, e^{4} + 21} + 4\right )}}{{\left (25 \, x - 25 \, e^{4} + 21\right )}^{2}} + \frac {187500 \, x e^{\left (\frac {25 \, x}{25 \, x - 25 \, e^{4} + 21} + 8\right )}}{25 \, x - 25 \, e^{4} + 21} - \frac {2343750 \, x^{2} e^{\left (\frac {25 \, x}{25 \, x - 25 \, e^{4} + 21} + 8\right )}}{{\left (25 \, x - 25 \, e^{4} + 21\right )}^{2}} - \frac {315000 \, x e^{\left (\frac {25 \, x}{25 \, x - 25 \, e^{4} + 21} + 4\right )}}{25 \, x - 25 \, e^{4} + 21} + \frac {3937500 \, x^{2} e^{\left (\frac {25 \, x}{25 \, x - 25 \, e^{4} + 21} + 4\right )}}{{\left (25 \, x - 25 \, e^{4} + 21\right )}^{2}} + \frac {198450 \, x}{25 \, x - 25 \, e^{4} + 21} - 5625 \, e^{8} + 9450 \, e^{4} - 441 \, e^{\left (\frac {50 \, x}{25 \, x - 25 \, e^{4} + 21}\right )} - 2646 \, e^{\left (\frac {25 \, x}{25 \, x - 25 \, e^{4} + 21}\right )} - 625 \, e^{\left (\frac {50 \, x}{25 \, x - 25 \, e^{4} + 21} + 8\right )} + 1050 \, e^{\left (\frac {50 \, x}{25 \, x - 25 \, e^{4} + 21} + 4\right )} - 3750 \, e^{\left (\frac {25 \, x}{25 \, x - 25 \, e^{4} + 21} + 8\right )} + 6300 \, e^{\left (\frac {25 \, x}{25 \, x - 25 \, e^{4} + 21} + 4\right )} - 3969}{9 \, {\left (\frac {15625 \, x^{2} e^{12}}{{\left (25 \, x - 25 \, e^{4} + 21\right )}^{2}} - \frac {39375 \, x^{2} e^{8}}{{\left (25 \, x - 25 \, e^{4} + 21\right )}^{2}} + \frac {33075 \, x^{2} e^{4}}{{\left (25 \, x - 25 \, e^{4} + 21\right )}^{2}} - \frac {9261 \, x^{2}}{{\left (25 \, x - 25 \, e^{4} + 21\right )}^{2}}\right )} {\left (25 \, e^{4} - 21\right )}} \]
Giac 1.7.0 via sagemath 9.3 output
\[ \text {Timed out} \]________________________________________________________________________________________