5.5 The Substitution Rule/27: Difference between revisions
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& \int{tdt} \\[2ex] | & \int{tdt} \\[2ex] | ||
& \cfrac{t^2}{2} | & \cfrac{t^2}{2} \\[2ex] | ||
& Substitute back t=\sqrt[3]{1+z^3} | |||
&= \cfrac\sqrt[3]{(1+z^3)^2}{2} + C | &= \cfrac\sqrt[3]{(1+z^3)^2}{2} + C | ||
Revision as of 21:12, 6 September 2022
![{\displaystyle {\begin{aligned}&\int {\cfrac {z^{2}}{\sqrt[{3}]{1+z^{3}}}}dz\\[2ex]&\int {tdt}\\[2ex]&{\cfrac {t^{2}}{2}}\\[2ex]&Substitutebackt={\sqrt[{3}]{1+z^{3}}}&={\cfrac {\sqrt[{3}]{(1+z^{3})^{2}}}{2}}+C\end{aligned}}}](https://en.wikipedia.org/api/rest_v1/media/math/render/svg/36f18154980cbdf83b82aac7770622d98e6fda01)