5.5 The Substitution Rule/3

$\int x^{2}{\sqrt {x^{3}+1}}dx$

${\begin{aligned}u&=x^{3}+1\\[2ex]du&=3x^{2}dx\end{aligned}}$

$\int {\frac {1}{3}}du{\sqrt {u}}$

<math> \frac{1}{3} \int du (u^{\frac{1}{2}}