It's a simple question we have :
$$\int_{0}^{\infty}3\Big(\frac{e^{-x^3}}{x+1}+\frac{xe^{-x^3}}{x^3+1}-\frac{e^{-x^3}}{x^3+1}\Big)dx=G$$
Where $G$ is the Gompertz constant
It has a simple antiderivative wich is equal to : $$eE_i(-x^3-1)$$
Where $E_i(x)$ is the Exponential integral
Applying the Fundamental theorem of calculus we get the desired result .
My question :
Have you another way to prove it ?
Thanks in advance for all your contributions.