From Mr. V Wiki Math
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| \begin{aligned} | | \begin{aligned} |
| u & = \ln^{2}{(x)} & x &= \tfrac{1}{\sqrt{2}}(u+v) \\[0.6ex] | | u & = \ln^{2}{(x)} & dv &= dx \\[0.6ex] |
| du & = \tfrac{2}{\ln{(x)}}dx & y &= \tfrac{1}{\sqrt{2}}(u-v) | | du & = \tfrac{2}{\ln{(x)}}dx & v &= x |
| \end{aligned} | | \end{aligned} |
| } | | } |
Revision as of 17:50, 29 November 2022
![{\displaystyle {\begin{aligned}\int \ln(x)^{3}dx&=x\ln(x)^{3}-3\underbrace {\int \ln(x)^{2}dx} _{\begin{aligned}u&=\ln ^{2}{(x)}&dv&=dx\\[0.6ex]du&={\tfrac {2}{\ln {(x)}}}dx&v&=x\end{aligned}}\end{aligned}}}](https://en.wikipedia.org/api/rest_v1/media/math/render/svg/d0f73c8866120b8490bbca8cb1685e7f38c04c2e)