$\displaystyle \int x^5(x^3+1)^{1/3}dx$
Integrands with radicals can often be simplified by substituting $\displaystyle u$ for the radical. This integral can be calculated by letting $\displaystyle u=(x^3+1)^{\frac{1}{3}}$.
The next step is to cube both sides, $\displaystyle u^3=x^3+1$, and relate the differentials.