How about first taking from within the square root, and move it outside as :
where , because we find ourselves in the range . This last expression can be more easily integrated. I suggest substitution.
This really took me by surprise, though I think it doesn't matter here since the even thing was just to change the integral's limits.
In fact I should have writtent , but in this case is irrelevant since the
variable t is already positive in the new integration's limits.
Tonio