5.5 The Substitution Rule/27: Difference between revisions

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& \cfrac{t^2}{2} \\[2ex]
& \cfrac{t^2}{2} \\[2ex]


&  \text{Substitute}t=\sqrt[3]{1+z^3}\text \\[2ex]
&  \text{Substitute}t\text=\sqrt[3]{1+z^3} \\[2ex]


&= \cfrac\sqrt[3]{(1+z^3)^2}{2} + C
&= \cfrac\sqrt[3]{(1+z^3)^2}{2} + C

Revision as of 21:40, 6 September 2022

Failed to parse (unknown function "\begin{align}"): {\displaystyle \begin{align} & \int \cfrac{z^2}{\sqrt[3]{1+z^3}} dz \\[2ex] & \int{tdt} \\[2ex] & \cfrac{t^2}{2} \\[2ex] & \text{Substitute}t\text=\sqrt[3]{1+z^3} \\[2ex] &= \cfrac\sqrt[3]{(1+z^3)^2}{2} + C \end{align} }