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} | ||
& | u &=1+{z}^3 | ||
du &=3{z}^2dz | |||
& | \frac{1}{3}du &={z}^2dz \\[2ex] | ||
& | |||
\end{align} | \end{align} | ||
</math> | </math> | ||
Revision as of 16:04, 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}du&=3{z}^{2}dz{\frac {1}{3}}du&={z}^{2}dz\\[2ex]\end{aligned}}}](https://en.wikipedia.org/api/rest_v1/media/math/render/svg/59bbb20d05a2789e16930d5feee7da94bb174d8b)