# Indefinite integral

• Feb 17th 2009, 03:37 PM
Larrioto
Indefinite integral
$\int x^5(x^3+1)^{1/3}dx$
• Feb 17th 2009, 04:23 PM
Scott H
Integrands with radicals can often be simplified by substituting $u$ for the radical. This integral can be calculated by letting $u=(x^3+1)^{\frac{1}{3}}$.

The next step is to cube both sides, $u^3=x^3+1$, and relate the differentials.