∫ z 2 1 + z 3 3 d z ∫ t d t t 2 2 [ S u b s t i t u t e ] t = 1 + z 3 3 = ( 1 + z 3 ) 2 3 2 + C {\displaystyle {\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}}}
![{\displaystyle {\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}}}](https://en.wikipedia.org/api/rest_v1/media/math/render/svg/d915f5c28602ed62d17f8f091ffd40a2fd695961)