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 (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://en.wikipedia.org/api/rest_v1/":): {\displaystyle \begin{align} & \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{align} }