\[ \int \frac {e^{-x^2} x \left (2 x^2+e^{2+2 e^{e^3}} \left (-2+2 x^2\right )+e^2 \left (-8+6 x^2+2 x^4\right )+e^{e^{e^3}} \left (-2 x+e^2 \left (4 x-4 x^3\right )\right )\right )+e^{-x^2} x \left (8-6 x^2-2 x^4+e^{2 e^{e^3}} \left (2-2 x^2\right )+e^{e^{e^3}} \left (-4 x+4 x^3\right )\right ) \log \left (4+e^{2 e^{e^3}}-2 e^{e^{e^3}} x+x^2\right )}{4+e^{2 e^{e^3}}-2 e^{e^{e^3}} x+x^2} \, dx \]
Optimal antiderivative \[ {\mathrm e}^{\ln \left (x \right )-x^{2}} \left (\ln \left (\left ({\mathrm e}^{{\mathrm e}^{{\mathrm e}^{3}}}-x \right )^{2}+4\right )-{\mathrm e}^{2}\right ) x \]
command
int((((-2*x^2+2)*exp(exp(exp(3)))^2+(4*x^3-4*x)*exp(exp(exp(3)))-2*x^4-6*x^2+8)*exp(ln(x)-x^2)*ln(exp(exp(exp(3)))^2-2*x*exp(exp(exp(3)))+x^2+4)+((2*x^2-2)*exp(2)*exp(exp(exp(3)))^2+((-4*x^3+4*x)*exp(2)-2*x)*exp(exp(exp(3)))+(2*x^4+6*x^2-8)*exp(2)+2*x^2)*exp(ln(x)-x^2))/(exp(exp(exp(3)))^2-2*x*exp(exp(exp(3)))+x^2+4),x,method=_RETURNVERBOSE)
Maple 2022.1 output
| method | result | size |
| risch | \(\left (-{\mathrm e}^{2} x +x \ln \left ({\mathrm e}^{2 \,{\mathrm e}^{{\mathrm e}^{3}}}-2 x \,{\mathrm e}^{{\mathrm e}^{{\mathrm e}^{3}}}+x^{2}+4\right )\right ) {\mathrm e}^{-x^{2}} x\) | \(36\) |
Maple 2021.1 output
hanged__________________________________________________________________________________