Integral Calculus: JEE Main 2023 Mathematics question

Let $f(x)=\frac{x}{\left(1+x^{n}\right)^{\frac{1}{n}}}, x \in \mathbb{R}-\{-1\}, n \in \mathbb{N}, n > 2$. If $f^{n}(x)=\left(f \circ f \circ f \ldots .\right.$. upto $n$ times) $(x)$, then \lim _\limits{n \rightarrow \infty} \int_\limits{0}^{1} x^{n-2}\left(f^{n}(x)\right) d x is equal to ____________.