7.1 Integration By Parts/20

$\int _{0}^{1}\left(x^{2}+1\right)e^{-x}dx$

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 \begin{align} u &= x^{2}+1 \quad dv= e^{-x}dx \\[2ex] du &= 2xdx \qquad v= -e^{-x} \\[2ex] \end{align} }

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 \begin{align} &= (x^{2}+1)(-e^{-x})\bigg|_{0}^{1} - 2\int_{0}^{1} (-e^{x})(x)dx \\[2ex] \end{align} }

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 \begin{align} u &= x \quad dv= -e^{-x}dx \\[2ex] du &= dx \qquad v= e^{-x} \\[2ex] \end{align} }

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 \begin{align} &= (x^{2}+1)(-e^{-x})\bigg|_{0}^{1} - 2\left[(x)(e^{-x})\right]\bigg|_{0}^{1} - \int_{0}^{1} (e^{-x})dx \\[2ex] &= (-2e^{-1}+1) - \frac{2}{e} \end{align} }