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| <math> | | <math> |
| \begin{align} | | \begin{align} |
| \int x^3(2+x^4)^5dx &= \int (x^3dx)(2+x^4) = \int \left(\frac{1}{4}du\right)(u) = \frac{1}{4}\int u\,du \\[2ex]
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| &= \frac{1}{4} \left[\frac{u^{1+1}}{1+1}\right] + C = \frac{u^2}{8} + C \\[2ex]
| | \int \frac{\sin{(\ln{(x))}}}{x}dx = \int\frac{1}{x}\sin(\ln{(x)})dx |
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| &= \frac{(2+x^4)^2}{8} + C
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| \end{align} | | \end{align} |
| </math> | | </math> |
Revision as of 19:04, 26 August 2022
![{\displaystyle {\begin{aligned}u&=\ln(x)\\[2ex]du&={\frac {1}{x}}dx\\[2ex]\end{aligned}}}](https://en.wikipedia.org/api/rest_v1/media/math/render/svg/2dcd1cacb47fe0ded9f0cb8411297ff136d61465)
