From Burton Tech. Points Wiki
Jump to navigation
Jump to search
|
|
| (7 intermediate revisions by 2 users not shown) |
| Line 17: |
Line 17: |
| \begin{align} | | \begin{align} |
|
| |
|
| \int(u)^{20}/frac{1}{3}du \\[2ex] | | \int u^{20}\cdot\frac{1}{3}du \\[2ex] |
| | &= \frac{1}{3}\int u^{20}du |
|
| |
|
| &= \int (du)\sin{(u)} = \int \sin{(u)}du \\[2ex] | | &= \frac{1}{3}\cdot\frac{1}{20+1} u^{20+1} |
| &= -\cos{(u)} + C \\[2ex] | | &= \frac{1}{3}\cdot\frac{1}{21} u^{21} |
| &= -\cos{(\ln{(x)})} + C | | &= \frac{1}{63} u^{21} + c |
| | &= \frac{1}{63} (3x-2)^{21} + c |
|
| |
|
| \end{align} | | \end{align} |
| | </math> |
| | |
| | <math> |
| | =\frac{1}{63} (3x^21-2097152) + c |
| </math> | | </math> |
Latest revision as of 19:37, 20 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}\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{aligned}}}](https://en.wikipedia.org/api/rest_v1/media/math/render/svg/504d7bdccf3dc2ef9663dd875868f1329b9c7594)
