Try Integration by Substitution, which is basically the Chain Rule backward:
Letting , we can see that , so that the integral becomes
Hope this helps.
Except that he didn't actually change the variable, so it was ok. This is how I would keep track of it...
(As usual straight continuous lines diff or anti-diff with respect to x, straight dashed lines with respect to the dashed balloon expression.)
Don't integrate - balloontegrate! Balloon Calculus: worked examples from past papers