y = x e − 0.4 x x = 0 , x = 1 {\displaystyle y=xe^{-0.4x}~~~x=0,x=1}
∫ 0 5 x e − 0.4 x d x ⏟ u = x d v = e − 0.4 x d x d u = d x v = 5 2 e − 0.4 x {\displaystyle {\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}}}
[ 5 2 e − 0.4 x ] + ∫ 5 0 5 2 e − 0.4 x d x {\displaystyle \left[{\frac {5}{2}}e^{-0.4x}\right]+\int _{5}^{0}{\frac {5}{2}}e^{-0.4x}dx}
u = − 0.4 x d u = d x {\displaystyle {\begin{aligned}u&=-0.4x\\[2ex]du&=dx\\[2ex]\end{aligned}}}
![{\displaystyle {\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}}}](https://en.wikipedia.org/api/rest_v1/media/math/render/svg/91d4a6c6285a2e1341ff3df89604c6777da55fd6)
![{\displaystyle \left[{\frac {5}{2}}e^{-0.4x}\right]+\int _{5}^{0}{\frac {5}{2}}e^{-0.4x}dx}](https://en.wikipedia.org/api/rest_v1/media/math/render/svg/4afefe06edf9bd3affd7c306ac9be17807450731)
![{\displaystyle {\begin{aligned}u&=-0.4x\\[2ex]du&=dx\\[2ex]\end{aligned}}}](https://en.wikipedia.org/api/rest_v1/media/math/render/svg/c92fde9fcc3d8607431d15850cf02eab037f5d7d)