1.
Let f:[1,)Rf : [1, \infty) \to \mathbb{R} be a differentiable function such that f(1)=13f(1) = \frac{1}{3} and 31xf(t)dt=xf(x)x333\int_1^x f(t)\,dt = x f(x) - \frac{x^3}{3}, x[1,)x\in[1,\infty). Then the value of f(e)f(e) is