You can integrate , whereas you cannot directly integrate
Integration is always a bit of guess and check. One might also consider letting or letting because we ultimately want to simplify the radical on the denominator to get it into a form that we can directly integrate. Will my alternative suggestions work? I have no idea (although the former would be particularly ill-advised here!), but they would remove the problem caused by the radical so they would be logical guesses. When dealing with radicals, setting (or ) equal to whatever is beneath the radical is usually a wise "first choice". You never "know" they will work for certain, but that's the joy of integration!