7.1 Integration By Parts/53

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

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

$\left[{\frac {5}{2}}e^{-0.4x}\right]+\int _{5}^{0}{\frac {5}{2}}e^{-0.4x}dx$ ${\begin{aligned}u&=-0.4x\\[2ex]du&=dx\\[2ex]2r\cdot dr&=du\\[2ex]\end{aligned}}$