7.1 Integration By Parts/48

Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://en.wikipedia.org/api/rest_v1/":): {\displaystyle \int_{}^{} \left(x^{n} e^{x} \right)dx = x^{n} e^{x} - n\int_{}^{} \left(x^{n-1} e^{x}\right)dx }

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