TITLE: Integral versus hypergeometric series: how to solve this?
QUESTION [5 upvotes]: How can I resolve the following indefinite integral using hypergeometric series?
$$
\int (x^3 + 1)^\frac{1}{3} \,dx
$$
Wolfram Alpha indicates that the series of Appell are used, but how to get to this result? 
Grateful!

REPLY [3 votes]: But how to get to this result?

By expanding the integrand into its binomial series, and switching the order of summation and integration.