5.5 The Substitution Rule/9: Difference between revisions
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\begin{align} | \begin{align} | ||
\int u^{20}\cdot\frac{1}{3}du \\[2ex] &= \frac{1}{3}\int u^{20}du | \int u^{20}\cdot\frac{1}{3}du \\[2ex] | ||
&= \frac{1}{3}\int u^{20}du | |||
&= \frac{1}{3}\cdot\frac{1}{20+1} u^{20+1} | &= \frac{1}{3}\cdot\frac{1}{20+1} u^{20+1} | ||
Revision as of 19:27, 20 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 (3x-2)^{20} dx }
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 &=3x-2 \\[2ex] du &= 3dx \\[2ex] \frac{1}{3}du &= dx \\[2ex] \end{align} }
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 u^{20}\cdot\frac{1}{3}du \\[2ex] &= \frac{1}{3}\int u^{20}du &= \frac{1}{3}\cdot\frac{1}{20+1} u^{20+1} &= \frac{1}{3}\cdot\frac{1}{21} u^{21} &= \frac{1}{63} u^{21} + c &= \frac{1}{63} (3x-2)^{21} + c \end{align} }