7.1 Integration By Parts/48

$\int _{}^{}\left(x^{n}e^{x}\right)dx=x^{n}e^{x}-n\int _{}^{}\left(x^{n-1}e^{x}\right)dx$

Failed to parse (Conversion error. Server ("https://en.wikipedia.org/api/rest_") reported: "Cannot get mml. Server problem."): {\displaystyle {\begin{aligned}u&=x^{n}\quad dv=e^{x}dx\\[2ex]du&=nx^{n-1}dx\quad v=e^{x}\\[2ex]\end{aligned}}}

Failed to parse (Conversion error. Server ("https://en.wikipedia.org/api/rest_") reported: "Cannot get mml. Server problem."): {\displaystyle {\begin{aligned}\int _{}^{}\left(x^{n}e^{x}\right)dx&=x^{n}e^{x}-\int _{}^{}\left(nx^{n-1}e^{x}\right)dx\\[2ex]&=x^{n}e^{x}-n\int _{}^{}\left(x^{n-1}e^{x}\right)dx\\[2ex]\end{aligned}}}