7.1 Integration By Parts/4

$\int (xe^{-x})dx$

$u=x\qquad dv=e^{-x}$

$du=dx\qquad v=-e^{-x}$

$\int (xe^{-x})dx=x(-e^{-x})-\int (-e^{-x})=-xe^{-x}-\int (-e^{-x})dx$

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 =-xe^{-x}+\int (e^{-x})dx = -xe^{-x}-e^{-x}+C} 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 -e^{-x}(x+1)+C }