\[ \int \frac {\left (-120 x^2+240 x^3-40 x^4+e \left (24-24 x^2-16 x^3\right )\right ) \log (2)}{225 x^2-150 x^3+25 x^4+e^2 \left (1+2 x+x^2\right )+e \left (-30 x-20 x^2+10 x^3\right )} \, dx \]
Optimal antiderivative \[ \frac {8 x \left (-x^{2}+3\right ) \ln \left (2\right )}{{\mathrm e}-\left (15-5 x -{\mathrm e}\right ) x} \]
command
integrate(((-16*x^3-24*x^2+24)*exp(1)-40*x^4+240*x^3-120*x^2)*log(2)/((x^2+2*x+1)*exp(1)^2+(10*x^3-20*x^2-30*x)*exp(1)+25*x^4-150*x^3+225*x^2),x, algorithm="giac")
Giac 1.9.0-11 via sagemath 9.6 output
\[ -\frac {8}{25} \, {\left (5 \, x + \frac {x e^{2} - 35 \, x e + 150 \, x + e^{2} - 15 \, e}{5 \, x^{2} + x e - 15 \, x + e}\right )} \log \left (2\right ) \]
Giac 1.7.0 via sagemath 9.3 output
\[ \int -\frac {8 \, {\left (5 \, x^{4} - 30 \, x^{3} + 15 \, x^{2} + {\left (2 \, x^{3} + 3 \, x^{2} - 3\right )} e\right )} \log \left (2\right )}{25 \, x^{4} - 150 \, x^{3} + 225 \, x^{2} + {\left (x^{2} + 2 \, x + 1\right )} e^{2} + 10 \, {\left (x^{3} - 2 \, x^{2} - 3 \, x\right )} e}\,{d x} \]________________________________________________________________________________________