7.1 Integration By Parts/51b: Difference between revisions
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\begin{align} | \begin{align} | ||
\int\ln(x)^3dx &= x\ln(x)^3 -3\underbrace{\int\ln(x)^2dx}_{ | \int\ln(x)^3dx &= x\ln(x)^3 -3\underbrace{\int\ln(x)^2dx}_{ | ||
\begin{aligned} | \begin{aligned} | ||
| Line 12: | Line 12: | ||
du & = \tfrac{2\ln{(x)}}{x}dx & v &= x | du & = \tfrac{2\ln{(x)}}{x}dx & v &= x | ||
\end{aligned} | \end{aligned} | ||
} | } \\ | ||
&= \int\ln(x)^3dx = x\ln(x)^3 -3 | &= \int\ln(x)^3dx = x\ln(x)^3 -3 | ||
Revision as of 17:52, 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)}}{x}}dx&v&=x\end{aligned}}\\&=\int \ln(x)^{3}dx=x\ln(x)^{3}-3\end{aligned}}}](https://en.wikipedia.org/api/rest_v1/media/math/render/svg/d1551eebe80285c70c1d4dc1036eb1c2d4b8f814)