Find the following general anti-derivatives using integration by parts formula a. intergration sign goes before problem but couldnt enter it on here (x+2/e^3x) dx
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$\displaystyle \int {\frac{{x + 2}} {{e^{3x} }}\,dx} = \int {xe^{ - 3x} \,dx} + 2\int {e^{ - 3x} \,dx} .$ The first one requires integration by parts.
$\displaystyle \int(x+2)e^{-3x}dx$ Let $\displaystyle u=x+2, \;\ dv=e^{-3x}dx, \;\ du=dx, \;\ v=\frac{-1}{3}e^{-3x}$ This gives: $\displaystyle (x+2)(\frac{-1}{3}e^{-3x})+\frac{1}{3}\int{e^{-3x}}dx$ Now, finish?.
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