7.1 Integration By Parts/47: Difference between revisions
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\int_{}^{} \left(\ln(x)^{n}\right)dx = x\left(\ln(x)^{n}\right)-n\int_{}^{}\left(\ln(x)^{n-1}\right)dx | \int_{}^{} \left(\ln(x)^{n}\right)dx = x\left(\ln(x)^{n}\right)-n\int_{}^{}\left(\ln(x)^{n-1}\right)dx | ||
</math> | |||
<math> | |||
\begin{align} | |||
u &= \ln(x)^{n} \quad dv= 1dx \\[2ex] | |||
du &=1dx \quad v=x \\[2ex] | |||
\end{align} | |||
</math> | </math> | ||
Revision as of 19:05, 28 November 2022
![{\displaystyle {\begin{aligned}u&=\ln(x)^{n}\quad dv=1dx\\[2ex]du&=1dx\quad v=x\\[2ex]\end{aligned}}}](https://en.wikipedia.org/api/rest_v1/media/math/render/svg/277e1db59ebb3040e84736b72d9f055c6ec9f9d3)