7.1 Integration By Parts/53

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

$\underbrace {\int _{0}^{5}xe^{-0.4x}dx}$

${\begin{aligned}u&=x\quad dv=e^{-0.4x}dx\\[2ex]du&=dx\qquad v={\frac {5}{2}}e^{-0.4x}\\[2ex]\end{aligned}}$

$\left[{\frac {5}{2}}e^{-0.4x}\right]+\int _{5}^{0}{\frac {5}{2}}e^{-0.4x}dx$