\[ \int \frac {e^{\frac {-50 x-2 x^2}{-43-53 x-2 x^2+e^x \left (50 x+2 x^2\right )}} \left (2150+172 x+6 x^2+e^x \left (2500 x^2+200 x^3+4 x^4\right )\right )}{1849+4558 x+2981 x^2+212 x^3+4 x^4+e^x \left (-4300 x-5472 x^2-412 x^3-8 x^4\right )+e^{2 x} \left (2500 x^2+200 x^3+4 x^4\right )} \, dx \]
Optimal antiderivative \[ {\mathrm e}^{\frac {x}{1-{\mathrm e}^{x} x +x +\frac {-7+x}{2 x +50}}} \]
command
integrate(((4*x^4+200*x^3+2500*x^2)*exp(x)+6*x^2+172*x+2150)*exp((-2*x^2-50*x)/((2*x^2+50*x)*exp(x)-2*x^2-53*x-43))/((4*x^4+200*x^3+2500*x^2)*exp(x)^2+(-8*x^4-412*x^3-5472*x^2-4300*x)*exp(x)+4*x^4+212*x^3+2981*x^2+4558*x+1849),x, algorithm="giac")
Giac 1.9.0-11 via sagemath 9.6 output
\[ e^{\left (-\frac {2 \, x^{2}}{2 \, x^{2} e^{x} - 2 \, x^{2} + 50 \, x e^{x} - 53 \, x - 43} - \frac {50 \, x}{2 \, x^{2} e^{x} - 2 \, x^{2} + 50 \, x e^{x} - 53 \, x - 43}\right )} \]
Giac 1.7.0 via sagemath 9.3 output
\[ \int \frac {2 \, {\left (3 \, x^{2} + 2 \, {\left (x^{4} + 50 \, x^{3} + 625 \, x^{2}\right )} e^{x} + 86 \, x + 1075\right )} e^{\left (\frac {2 \, {\left (x^{2} + 25 \, x\right )}}{2 \, x^{2} - 2 \, {\left (x^{2} + 25 \, x\right )} e^{x} + 53 \, x + 43}\right )}}{4 \, x^{4} + 212 \, x^{3} + 2981 \, x^{2} + 4 \, {\left (x^{4} + 50 \, x^{3} + 625 \, x^{2}\right )} e^{\left (2 \, x\right )} - 4 \, {\left (2 \, x^{4} + 103 \, x^{3} + 1368 \, x^{2} + 1075 \, x\right )} e^{x} + 4558 \, x + 1849}\,{d x} \]________________________________________________________________________________________