7.1 Integration By Parts/53

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

Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://en.wikipedia.org/api/rest_v1/":): {\displaystyle \underbrace{\int_{0}^{5}xe^{-0.4x}dx}_{ \begin{align} \begin{aligned} u &= x \quad dv= e^{-0.4x} dx \\[0.6ex] du &= dx \qquad v= \frac{5}{2}e^{-0.4x} \end{aligned} \\[2ex] \end{align} }

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