Derivatives by Parts

[Alpha6]

I'd like some feedback as to whether or not I'm doing this correctly:

So I learned the equation for derivatives by parts is uv - ſ vdu dx

For the equation X² e^x

I did:

u = x² dv = e^x

du = 2x v = e^x


= x² (e^x) - ſ e^x (2x) dx

Am I doing it right so far? Also, I need to now use the same rule on the "ſ e^x (2x) dx" part now right?

Help please.

 

[HallsofIvy]

Yes, that's exactly right.

 

[Ishuda]

I'd like some feedback as to whether or not I'm doing this correctly:

So I learned the equation for derivatives by parts is uv - ſ vdu dx

For the equation X² e^x

I did:

u = x² dv = e^x

du = 2x v = e^x


= x² (e^x) - ſ e^x (2x) dx

Am I doing it right so far? Also, I need to now use the same rule on the "ſ e^x (2x) dx" part now right?Help please.

Basically, yes. The notation is a little off but you have the right idea:
\(\displaystyle \int u\space \frac{dv}{dx}\space dx = u\space v - \int v\space \frac{du}{dx}\space dx\)
or it is also written as
\(\displaystyle \int\space u\space dv = u\space v - \int\space v\space du\)

Oh, and it is integration by parts, not derivatives by parts.