Definite Integration

Let \(f: \mathbb{R} \rightarrow \mathbb{R}\) be a function defined by \(f(x)=\frac{x}{\left(1+x^4\right)^{1 / 4}}\), and \(g(x)=f(f(f(f(x))))\). Then, \(18 \int_0^{\sqrt{2 \sqrt{5}}} x^2 g(x) d x\) is equal to