Let's do some calculus! (5)

Calculus Level 4

\[\begin{align} f(x) & =\dfrac{x}{{\left(1+x^{n}\right)}^{{1}/{n}}} & \forall ~n \ge 2 \\ g(x) & =\underbrace{f \circ f \circ f \circ \cdots f}_{f \text{ occurs } n \text{ times}}\left(x\right) \end{align} \]

For functions \(f\) and \(g\) as defined above, which of the following is an antiderivative of \(\displaystyle \int x^{n-2} g(x) \, dx \)?

Clarification: \(C\) denotes the arbitrary constant of integration.

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