5.5 The Substitution Rule/27: Difference between revisions

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<math>
\int \cfrac{z^2}{\sqrt[3]{1+z^3}} dz
</math>
<math>
<math>
\begin{align}
\begin{align}


& \int \cfrac{z^2}{\sqrt[3]{1+z^3}} dz \\[2ex]
u &=1+{z}^3
 
du &=3{z}^2dz
& \int{tdt} \\[2ex]
\frac{1}{3}du &={z}^2dz \\[2ex]
 
& \cfrac{t^2}{2} \\[2ex]
 
& \text{Substitute }t=\sqrt[3]{1+z^3} \\[2ex]
 
&= \cfrac\sqrt[3]{(1+z^3)^2}{2} + C
 
 
 
 


\end{align}
\end{align}
</math>
</math>

Revision as of 16:04, 7 September 2022

Failed to parse (Conversion error. Server ("https://en.wikipedia.org/api/rest_") reported: "Cannot get mml. Server problem."): {\displaystyle {\begin{aligned}u&=1+{z}^{3}du&=3{z}^{2}dz{\frac {1}{3}}du&={z}^{2}dz\\[2ex]\end{aligned}}}

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