7.1 Integration By Parts/48

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

${\begin{aligned}u&=x^{n}\quad dv=e^{x}dx\\[2ex]du&=nx^{n-1}dx\quad v=e^{x}\\[2ex]\end{aligned}}$

\int_{}^{} \left(x^{n} e^{x} \right)dx = n^{n}e^{x} - \int_{}^{} \left(x^{n-1}e^{x}\right)dx

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