Primitive function/Roots/Via primitive function of inverse mapping/Exercise

Let ${}n\in \mathbb {N} _{+}$. Determine an antiderivative of the function

$\mathbb {R} _{+}\longrightarrow \mathbb {R} _{+},x\longmapsto x^{1/n},$

using the antiderivative of ${}x^{n}$ and

the theorem about integration of inverse function.

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