5.5 The Substitution Rule/27

${\begin{aligned}&\int {\cfrac {z^{2}}{\sqrt[{3}]{1+z^{3}}}}dz\\[2ex]&\int {tdt}\\[2ex]&{\cfrac {t^{2}}{2}}\\[2ex]&Substitute\\t={\sqrt[{3}]{1+z^{3}}}\\[2ex]&={\cfrac {\sqrt[{3}]{(1+z^{3})^{2}}}{2}}+C\end{aligned}}$