For the following indefinite integral, find the full power series centered at $x=0$ and then give the first 5 nonzero terms of the power series.

$$f(x) = \int x^{6} \sin (x^{3})\ dx$$

$f(x) = C + \displaystyle\sum\limits_{n=0}^{\infty}$

$f(x) = C +$ $+$ $+$ $+$ $+$ $+ \cdots$