5.5 The Substitution Rule/27: Difference between revisions
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& \cfrac{t^2}{2} \\[2ex] | & \cfrac{t^2}{2} \\[2ex] | ||
& Substitute t=\sqrt[3]{1+z^3} \\[2ex] | & Substitute\\\\t=\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 21:14, 6 September 2022
Failed to parse (Conversion error. Server ("https://en.wikipedia.org/api/rest_") reported: "Cannot get mml. Server problem."): {\displaystyle {\begin{aligned}&\int {\cfrac {z^{2}}{\sqrt[{3}]{1+z^{3}}}}dz\\[2ex]&\int {tdt}\\[2ex]&{\cfrac {t^{2}}{2}}\\[2ex]&Substitute\\\\t={\sqrt[{3}]{1+z^{3}}}\\[2ex]&={\cfrac {\sqrt[{3}]{(1+z^{3})^{2}}}{2}}+C\end{aligned}}}