Where Does the du/2 Come From in the Integral of a Product?

[Ry122]

In the following problem where does the du/2 come from?
I don't understand why it isn't just du.
http://users.on.net/~rohanlal/partialdif.jpg

 

[danago]

They have made the substitution u = x^2+1, hence the corrosponding differential du is given by:

du = 2x dx

Hence, after rearranging:

dx = du / 2x

Sub this back into the integral, and the x's will cancel out, leaving du/2.

 

[Ry122]

when differentiating u why does it gain a dx?
dx is usually only present when attempting to find the integral of something, not when stating the derivative of a function.