Integration by parts(?)

1. Jul 23, 2011

Niles

1. The problem statement, all variables and given/known data
Hi

There is a step in my book, which I can't follow. It is the following

$$\int_0^1 {w\left( {\frac{{d^2 u}}{{dx^2 }} - u + x} \right)dx} = \int_0^1 {\left( { - \frac{{dw}}{{dx}}\frac{{du}}{{dx}} - wu + xw} \right)dx} + \left[ {w\frac{{du}}{{dx}}} \right]_0^1$$

I thought they might be using integration by parts, but that doesn't seem to be correct. Any help is greatly appreciated.

Best,
Niles.

2. Jul 23, 2011

ehild

The first term, w u" is integrated by parts.

ehild

3. Jul 23, 2011

Niles

I see, thanks!

4. Jul 23, 2011

nickalh

If not, start to integrate the first term, w u'', by parts, & show us what you get.

5. Jul 23, 2011

Niles

Yes, I got it. Thanks to both of you.

Best,
Niles.