# Thread: Do not understand (integration by parts)

1. ## Do not understand (integration by parts)

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

2. $\int {\frac{{x + 2}}
{{e^{3x} }}\,dx} = \int {xe^{ - 3x} \,dx} + 2\int {e^{ - 3x} \,dx} .$

The first one requires integration by parts.

3. $\int(x+2)e^{-3x}dx$

Let $u=x+2, \;\ dv=e^{-3x}dx, \;\ du=dx, \;\ v=\frac{-1}{3}e^{-3x}$

This gives:

$(x+2)(\frac{-1}{3}e^{-3x})+\frac{1}{3}\int{e^{-3x}}dx$

Now, finish?.