If you post the problem, I could tell you for sure, but given an integrating factor of , I would simplify this to . The log and the exponential then cancel out to give you an integrating factor of . Is this the integrating factor that you actually got?

Secondly, how did your friend get ? Anycase, he is wrong, if you take the super complicated and long way around, you still get the integration of .

Out of interest, if you want to do the long way, let u = ln(t), hence t = exp(u) then let v =4u. Don't for get to change the dt in each case.