Let f:(0,∞)→(0,∞) be a differentiable function satisfying, xx∫0(1−t)f(t) dt=x∫0tf(t) dt,x∈R+ and f(1)=1, the value of f(x)=1xme(1−1/x), then m=

Let f:(0,∞)→(0,∞) be a differentiable function satisfying, xx∫

1.	Let f:(0,∞)→(0,∞) be a differentiable function satisfying, xx∫0(1−t)f(t) dt=x∫0tf(t) dt,x∈R+ and f(1)=1, the value of f(x)=1xme(1−1/x), then m=
Answer» Let $f : (0, \infty) \to (0, \infty)$ be a differentiable function satisfying, $x x \int 0 (1 - t) f (t) d t = x \int 0 t f (t) d t, x \in R^{+}$ and $f (1) = 1$ , the value of $f (x) = \frac{1}{x^{m}} e^{(1 - 1 / x)}$ , then $m =$