Variable change in definite integration

[bartrocs]

I am having trouble understanding how the author of the textbook "Physics for scientists and engineers" (Randall D Knight), is performing the variable change in the definite integral of the picture that I have taken a screen clipping of. Can someone please help me figure this out?

 

[grzz]

Variable r is being replaced by variable u where

u = z$^{2}$ + r$^{2}$.

Hence

$\frac{du}{dr}$ = 2r

since z is a constant.

 

[bartrocs]

thanks! I understand now