5.5 The Substitution Rule/27: Difference between revisions
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\begin{align} | \begin{align} | ||
\int \cfrac{z^2}{\sqrt[3]{1+z^3}} dz | \int \cfrac{z^2}{\sqrt[3]{1+z^3}} dz &= \frac{1}{3}\int\frac{1}{\sqrt[3]{u}}du | ||
\end{align} | \end{align} | ||
</math> | </math> | ||
Revision as of 16:24, 7 September 2022
![{\displaystyle \int {\cfrac {z^{2}}{\sqrt[{3}]{1+z^{3}}}}dz}](https://en.wikipedia.org/api/rest_v1/media/math/render/svg/a16762723c154c008294ac839f1997ba1455d543)
![{\displaystyle {\begin{aligned}u&=1+{z}^{3}\\[2ex]du&=3{z}^{2}dz\\[2ex]{\frac {1}{3}}du&={z}^{2}dz\\[2ex]\end{aligned}}}](https://en.wikipedia.org/api/rest_v1/media/math/render/svg/a2fa06923c4c79966cfebb815eb85a2321de6418)
![{\displaystyle {\begin{aligned}\int {\cfrac {z^{2}}{\sqrt[{3}]{1+z^{3}}}}dz&={\frac {1}{3}}\int {\frac {1}{\sqrt[{3}]{u}}}du\end{aligned}}}](https://en.wikipedia.org/api/rest_v1/media/math/render/svg/ce4c716009d35907c26819a5fe31a0217c01d01e)