5.5 The Substitution Rule/27: Difference between revisions

From Mr. V Wiki Math
Jump to navigation Jump to search
No edit summary
No edit summary
Line 1: Line 1:
<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 (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 \int \cfrac{z^2}{\sqrt[3]{1+z^3}} dz }

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} u &=1+{z}^3 du &=3{z}^2dz \frac{1}{3}du &={z}^2dz \\[2ex] \end{align} }