\[ \int \frac {-6 x+2 x^3+e^{10} \left (-6 x+2 x^3\right )+e^5 \left (-12 x+4 x^3\right )+e^{2-2 x} \left (-6 x+6 x^2+2 x^3-2 x^4\right )+e^{1-x} \left (-12 x+6 x^2+4 x^3-2 x^4+e^5 \left (-12 x+6 x^2+4 x^3-2 x^4\right )\right )+\left (2 x+2 x^3+4 e^5 x^3+2 e^{10} x^3+2 e^{2-2 x} x^3+e^{1-x} \left (4 x^3+4 e^5 x^3\right )\right ) \log \left (1+x^2+2 e^5 x^2+e^{10} x^2+e^{2-2 x} x^2+e^{1-x} \left (2 x^2+2 e^5 x^2\right )\right )}{1+x^2+2 e^5 x^2+e^{10} x^2+e^{2-2 x} x^2+e^{1-x} \left (2 x^2+2 e^5 x^2\right )} \, dx \]
Optimal antiderivative \[ \ln \! \left (1+x^{2} \left ({\mathrm e}^{1-x}+{\mathrm e}^{5}+1\right )^{2}\right ) \left (x^{2}-3\right ) \]
command
integrate(((2*x^3*exp(1-x)^2+(4*x^3*exp(5)+4*x^3)*exp(1-x)+2*x^3*exp(5)^2+4*x^3*exp(5)+2*x^3+2*x)*log(x^2*exp(1-x)^2+(2*x^2*exp(5)+2*x^2)*exp(1-x)+x^2*exp(5)^2+2*x^2*exp(5)+x^2+1)+(-2*x^4+2*x^3+6*x^2-6*x)*exp(1-x)^2+((-2*x^4+4*x^3+6*x^2-12*x)*exp(5)-2*x^4+4*x^3+6*x^2-12*x)*exp(1-x)+(2*x^3-6*x)*exp(5)^2+(4*x^3-12*x)*exp(5)+2*x^3-6*x)/(x^2*exp(1-x)^2+(2*x^2*exp(5)+2*x^2)*exp(1-x)+x^2*exp(5)^2+2*x^2*exp(5)+x^2+1),x, algorithm="giac")
Giac 1.9.0-11 via sagemath 9.6 output
\[ \text {Timed out} \]
Giac 1.7.0 via sagemath 9.3 output
\[ -2 \, x^{3} + x^{2} \log \left (x^{2} e^{2} + x^{2} e^{\left (2 \, x\right )} + x^{2} e^{\left (2 \, x + 10\right )} + 2 \, x^{2} e^{\left (2 \, x + 5\right )} + 2 \, x^{2} e^{\left (x + 6\right )} + 2 \, x^{2} e^{\left (x + 1\right )} + e^{\left (2 \, x\right )}\right ) + 6 \, x - 3 \, \log \left (x^{2} e^{2} + x^{2} e^{\left (2 \, x\right )} + x^{2} e^{\left (2 \, x + 10\right )} + 2 \, x^{2} e^{\left (2 \, x + 5\right )} + 2 \, x^{2} e^{\left (x + 6\right )} + 2 \, x^{2} e^{\left (x + 1\right )} + e^{\left (2 \, x\right )}\right ) \]