Why is the first term ignored in the group velocity derivation?

[chingel]

I was reading the derivation on Wikipedia:

http://en.wikipedia.org/wiki/Group_velocity#Derivation

Why is the first part before the integral sign ignored when calculating the velocity? Surely it would also cause a phase shift in some time interval and make the waves move forward (or backward)?

 

[mfb]

Group velocity cares about the speed of the amplitude, phases are not relevant for the group velocity.

 

[chingel]

Ok, but when calculating the velocity by dividing the terms in front of t by those in front of k, why can some of the terms in front of t be ignored?