Ok, so a teacher showed an example in class awhile back. So im going over my notes right now, and I don't understand a certain part of the problem. Also im new to the forums and its my first time posting here, so please push me in the right direction if i make a mistake. integration of (x-2)(1/2)/(x+2) the solution is: 2(x-2).5 - 4tan-1((x-2).5/2) + C Basically what i tried doing, is: u2 = x-2 u = (x-2).5 2u du = dx which after a few steps leads me to: 2u - 8(integration of (u2 +4)-1) After this i stop understanding the problem a little... From here i sub the root x-2 back in as u and u2 as x-2, which gives me: 2(x-2).5 - 8ln|x+2| which is wrong i think.... The way the example continues is as such: u2 = 4z2 u = 2z du = 2 dz 2u - ((8)(2)/4) integration of dz/ (z2 +1) which gives the answer given above... Basically i dont understand why we want to sub in another letter for u2, and why i cant get the same answer when i sub in the (x-2).5 earlier.