7.1 Integration By Parts/37
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Revision as of 02:37, 29 November 2022 by Elizabethh58413 (talk | contribs) (Created page with "<math> \int x\ln({x})dx </math> <br> <math> \begin{align} u &= x + 1 \\[2ex] x &= u-1 \\[2ex] du &= dx \\[2ex] \end{align} </math> <br> <math> \begin{align} \int(u-1)\ln({u}) du &= \ln{u} \cdot \frac{1}{2}u^2 - u \int(\frac{1}{2}u^2-u) \cdot \frac{1}{u} du \\[2ex]")
<math>
\begin{align}
\int(u-1)\ln({u}) du &= \ln{u} \cdot \frac{1}{2}u^2 - u \int(\frac{1}{2}u^2-u) \cdot \frac{1}{u} du \\[2ex]
![{\displaystyle {\begin{aligned}u&=x+1\\[2ex]x&=u-1\\[2ex]du&=dx\\[2ex]\end{aligned}}}](https://en.wikipedia.org/api/rest_v1/media/math/render/svg/384447aed379c8029bdd9f79fd82b9bec930cc01)