∫ ( ln ( x ) n ) d x = x ( ln ( x ) n ) − n ∫ ( ln ( x ) n − 1 ) d x {\displaystyle \int _{}^{}\left(\ln(x)^{n}\right)dx=x\left(\ln(x)^{n}\right)-n\int _{}^{}\left(\ln(x)^{n-1}\right)dx}
u = ln ( x ) n d v = 1 d x d u = 1 d x v = x {\displaystyle {\begin{aligned}u&=\ln(x)^{n}\quad dv=1dx\\[2ex]du&=1dx\quad v=x\\[2ex]\end{aligned}}}
![{\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)