\[ \int \frac {16 x-16 e x}{-1+e^3+12 x-48 x^2+64 x^3+e^2 (-3+12 x)+e \left (3-24 x+48 x^2\right )} \, dx \]
Optimal antiderivative \[ 2-\frac {8}{\left (4-\frac {1-{\mathrm e}}{x}\right )^{2}} \]
command
integrate((-16*x*exp(1)+16*x)/(exp(1)^3+(12*x-3)*exp(1)^2+(48*x^2-24*x+3)*exp(1)+64*x^3-48*x^2+12*x-1),x, algorithm="giac")
Giac 1.9.0-11 via sagemath 9.6 output
\[ \frac {8 \, x e - 8 \, x + e^{2} - 2 \, e + 1}{2 \, {\left (4 \, x + e - 1\right )}^{2}} \]
Giac 1.7.0 via sagemath 9.3 output
\[ \int -\frac {16 \, {\left (x e - x\right )}}{64 \, x^{3} - 48 \, x^{2} + 3 \, {\left (4 \, x - 1\right )} e^{2} + 3 \, {\left (16 \, x^{2} - 8 \, x + 1\right )} e + 12 \, x + e^{3} - 1}\,{d x} \]________________________________________________________________________________________