43.56 Problem number 8742

\[ \int \frac {e^{\frac {3 x+e^{200+40 x+2 x^2} x-\log \left (-2+e^2+e^5\right )}{x}} \left (e^{200+40 x+2 x^2} \left (40 x^2+4 x^3\right )+\log \left (-2+e^2+e^5\right )\right )}{x^2} \, dx \]

Optimal antiderivative \[ 1+{\mathrm e}^{{\mathrm e}^{2 \left (x +10\right )^{2}}-\frac {\ln \left ({\mathrm e}^{5}+{\mathrm e}^{2}-2\right )}{x}+3} \]

command

integrate((log(exp(5)+exp(2)-2)+(4*x^3+40*x^2)*exp(x^2+20*x+100)^2)*exp((-log(exp(5)+exp(2)-2)+x*exp(x^2+20*x+100)^2+3*x)/x)/x^2,x, algorithm="giac")

Giac 1.9.0-11 via sagemath 9.6 output

\[ \text {could not integrate} \]

Giac 1.7.0 via sagemath 9.3 output

\[ e^{\left (-\frac {\log \left (e^{5} + e^{2} - 2\right )}{x} + e^{\left (2 \, x^{2} + 40 \, x + 200\right )} + 3\right )} \]