Mathematics Question from JEE Main 2023 · 6 April, Shift 2

Let $f(x) = \dfrac{x}{\left(1 + x^{n}\right)^{1/n}}$, $x \in \mathbb{R} - \{-1\}$, $n \in \mathbb{N}$, $n > 2$. If $f^{n}(x) = (f \circ f \circ \cdots \text{ upto } n \text{ times})(x)$, then $\lim_{n \to \infty} \int_0^1 x^{n-2}\, f^{n}(x)\, dx$ is equal to _____ :