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| \begin{align} | | \begin{align} |
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| \int(u)^{20}/frac{1}{3}du \\[2ex] | | \int u^{20}\cdot\frac{1}{3}du \\[2ex] &= \frac{1}{3}\int u^{20}du |
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| &= \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 |
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| \end{align} | | \end{align} |
| </math> | | </math> |
Revision as of 04:05, 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}\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/c80ce381f4275be7a50c3739115f11b78d9715be)