# Let's do some calculus! (5)

Calculus Level 4

\begin{aligned} 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{aligned}

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.