5.5 The Substitution Rule/9: Difference between revisions
Jump to navigation
Jump to search
No edit summary |
No edit summary |
||
| Line 7: | Line 7: | ||
\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
![{\displaystyle {\begin{aligned}u&=3x-2\\[2ex]du&=3dx\\[2ex]{\frac {1}{3}}du&=dx\\[2ex]\end{aligned}}}](https://en.wikipedia.org/api/rest_v1/media/math/render/svg/45bebb73a627f87f28c7b799f9d7ce3e8d4e6fd5)
![{\displaystyle {\begin{aligned}\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{aligned}}}](https://en.wikipedia.org/api/rest_v1/media/math/render/svg/c6eafd29a3abde02df313123dcea5272279e590e)