5.5 The Substitution Rule/27

$\int {\cfrac {z^{2}}{\sqrt[{3}]{1+z^{3}}}}dz$

${\begin{aligned}u&=1+{z}^{3}\\[2ex]du&=3{z}^{2}dz\\[2ex]{\frac {1}{3}}du&={z}^{2}dz\\[2ex]\end{aligned}}$

Failed to parse (unknown function "\begin{align}"): {\displaystyle \begin{align} \int \cfrac{z^2}{\sqrt[3]{1+z^3}} dz &= \frac{1}{3}\int\frac{1}{\sqrt[3]{u}}du = \frac{1}{3}\int\{u}^-\frac{1}{3}du \\[2ex] &= -\frac{1}{3}(\frac{3}{2}{u}^\frac{2}{3}) = \frac{3}{6}{u}^2/3 \\[2ex] &= -\cos{(u)} + C \\[2ex] &= \frac{1}{2}{1+z^3}^\frac{2}{3} + C \end{align} }