7.1 Integration By Parts/53

$y=xe^{-0.4x}~~~x=0,x=1$

$\underbrace {\int _{0}^{5}xe^{-0.4x}dx}$ \begin{aligned} u & = \x & dv &= dx \\[0.6ex] du & = \tfrac{2\ln{(x)}}{x}dx & v &= x \end{aligned}} \\ [2ex]

\begin{aligned} u & = \ln^{2}{(x)} & dv &= dx \\[0.6ex] du & = \tfrac{2\ln{(x)}}{x}dx & v &= x \end{aligned}} \\ [2ex]