\[ \int \frac {-4 x^6+2 x^6 \log (2)+e^{4 x^2} \left (-4 x^2+2 x^2 \log (2)\right )+e^{3 x^2} \left (-16 x^3+8 x^3 \log (2)\right )+\left (-4 x^3-3 x^2 \log (2)\right ) \log (4)+e^{2 x^2} \left (-24 x^4+12 x^4 \log (2)+\left (-2 x-4 x^3+\left (-1-4 x^2\right ) \log (2)\right ) \log (4)\right )+e^{x^2} \left (-16 x^5+8 x^5 \log (2)+\left (-6 x^2-4 x^4+\left (-4 x-4 x^3\right ) \log (2)\right ) \log (4)\right )}{16 x^6+16 x^7+4 x^8+e^{4 x^2} \left (16 x^2+16 x^3+4 x^4\right )+e^{3 x^2} \left (64 x^3+64 x^4+16 x^5\right )+\left (8 x^3+4 x^4\right ) \log (4)+\log ^2(4)+e^{2 x^2} \left (96 x^4+96 x^5+24 x^6+\left (8 x+4 x^2\right ) \log (4)\right )+e^{x^2} \left (64 x^5+64 x^6+16 x^7+\left (16 x^2+8 x^3\right ) \log (4)\right )} \, dx \]
Optimal antiderivative \[ \frac {-x -\ln \left (2\right )}{2 x +\frac {2 \ln \left (2\right )}{\left ({\mathrm e}^{x^{2}}+x \right )^{2} x}+4} \]
command
integrate(((2*x^2*log(2)-4*x^2)*exp(x^2)^4+(8*x^3*log(2)-16*x^3)*exp(x^2)^3+(2*((-4*x^2-1)*log(2)-4*x^3-2*x)*log(2)+12*x^4*log(2)-24*x^4)*exp(x^2)^2+(2*((-4*x^3-4*x)*log(2)-4*x^4-6*x^2)*log(2)+8*x^5*log(2)-16*x^5)*exp(x^2)+2*(-3*x^2*log(2)-4*x^3)*log(2)+2*x^6*log(2)-4*x^6)/((4*x^4+16*x^3+16*x^2)*exp(x^2)^4+(16*x^5+64*x^4+64*x^3)*exp(x^2)^3+(2*(4*x^2+8*x)*log(2)+24*x^6+96*x^5+96*x^4)*exp(x^2)^2+(2*(8*x^3+16*x^2)*log(2)+16*x^7+64*x^6+64*x^5)*exp(x^2)+4*log(2)^2+2*(4*x^4+8*x^3)*log(2)+4*x^8+16*x^7+16*x^6),x, algorithm="giac")
Giac 1.9.0-11 via sagemath 9.6 output
\[ -\frac {x^{4} \log \left (2\right ) + 2 \, x^{3} e^{\left (x^{2}\right )} \log \left (2\right ) - 2 \, x^{4} - 4 \, x^{3} e^{\left (x^{2}\right )} + 2 \, x^{3} \log \left (2\right ) + x^{2} e^{\left (2 \, x^{2}\right )} \log \left (2\right ) + 4 \, x^{2} e^{\left (x^{2}\right )} \log \left (2\right ) - 4 \, x^{3} - 2 \, x^{2} e^{\left (2 \, x^{2}\right )} - 8 \, x^{2} e^{\left (x^{2}\right )} + 2 \, x e^{\left (2 \, x^{2}\right )} \log \left (2\right ) - 4 \, x e^{\left (2 \, x^{2}\right )} - 2 \, x \log \left (2\right ) - \log \left (2\right )^{2} - 2 \, \log \left (2\right )}{2 \, {\left (x^{5} + 2 \, x^{4} e^{\left (x^{2}\right )} + 4 \, x^{4} + x^{3} e^{\left (2 \, x^{2}\right )} + 8 \, x^{3} e^{\left (x^{2}\right )} + 4 \, x^{3} + 4 \, x^{2} e^{\left (2 \, x^{2}\right )} + 8 \, x^{2} e^{\left (x^{2}\right )} + 4 \, x e^{\left (2 \, x^{2}\right )} + x \log \left (2\right ) + 2 \, \log \left (2\right )\right )}} \]
Giac 1.7.0 via sagemath 9.3 output
\[ \text {Exception raised: TypeError} \]________________________________________________________________________________________