Strange Integral- Does it even exist?

[The_ArtofScience]

I was watching DonnyLee's videos on youtube and I noticed something strange. I think he picked u=x and du=dx, and if I'm right (?) he picked v= \int x dy/dx but does that even equal to y? But that can't be right because the right side kept the original expression. Some help might clear up the fuzziness
https://www.youtube.com/watch?v=<object width="425" height="344"><param name="movie" value="http://www.youtube.com/v/GAkkTa2XpEc&hl=en&fs=1"></param><param name="allowFullScreen" value="true"></param><embed src="http://www.youtube.com/v/GAkkTa2XpEc&hl=en&fs=1" type="application/x-shockwave-flash" allowfullscreen="true" width="425" height="344"></embed></object>

 

[spideyunlimit]

can't see any video... give the link

 

[The_ArtofScience]

LinK: http://www.youtube.com/watch?v=GAkkTa2XpEc"

 

[matticus]

I believe:

u = y. du = dy/dx * dx.
dv = d/dx* x * dx. v = x.