a) Đặt\(\left\{ \matrix{
u = x \hfill \cr
dv = {e^{ - x}}dx \hfill \cr} \right. \Rightarrow \left\{ \matrix{
du = dx \hfill \cr
v = - {e^{ - x}} \hfill \cr} \right.\)Suy ra \(\int {x{e^{ - x}}dx = - x{e^{ - x}} + \int {{e^{ - x}}dx = - x{e^{ - x}} - {e^{ - x}} + C = - {e^{ - x}}\left( {x + 1} \right) + C} } \)
b) Đặt \(u = \ln x \Rightarrow du = {{dx} \over x}\)Do đó \(\int {{{\ln x} \over x}} dx = \int {udu = {{{u^2}} \over 2}} + C = {{{{(\ln x)}^2}} \over 2} + C\)
