Let $X$ be a random variable with pdf $$ f(x)=\dfrac{\mathrm{e}^{-x}}{\left(\mathrm{e}^{-x}+1\right)^2}$$ $-\infty< x<\infty$, I have to find the mgf of $X$.
The question gives a hint: write in an integral that is a special type of function.
So I let $$u=\mathrm{e}^{-x}$$ and then substitute it in to the function and try to make a Gamma function but didn't work out...