Understanding Integration by Parts: Solving Tricky Integrals

[Niles]

Homework Statement

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.


Niles.

 

[ehild]

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

ehild

 

[Niles]

I see, thanks!

 

[nickalh]

Does that answer your question?
If not, start to integrate the first term, w u'', by parts, & show us what you get.

 

[Niles]

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