5.5 The Substitution Rule/9: Difference between revisions
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\begin{align} | \begin{align} | ||
u &=\ | u &=3x-2 \\[2ex] | ||
du &= \frac{1}{ | du &= 3dx \\[2ex] | ||
\frac{1}{3}du &= dx \\[2ex] | |||
\end{align} | |||
</math> | |||
<math> | |||
\begin{align} | |||
\int(u)^{20}/frac{1}{3}du \\[2ex] | |||
&= \int (du)\sin{(u)} = \int \sin{(u)}du \\[2ex] | |||
&= -\cos{(u)} + C \\[2ex] | |||
&= -\cos{(\ln{(x)})} + C | |||
\end{align} | \end{align} | ||
</math> | </math> | ||
Revision as of 03:53, 4 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}/frac{1}{3}du \\[2ex] &= \int (du)\sin{(u)} = \int \sin{(u)}du \\[2ex] &= -\cos{(u)} + C \\[2ex] &= -\cos{(\ln{(x)})} + C \end{align} }