Question. (Logistic Distribution). Consider the function given by f(x)=e^-x(1+e^-x)² for <x< . Prove that f is a density function.

I set f(x) 0 and +f(x)dx=1 and I got [((e^-x+1)³ / 3) + C ] + = 1 but I don't know how to prove that f is a density function.