Hi, so I've got a simple problem to evaluate the surface area for 1/x when rotated around the x axis. Ok, so that takes a quit bit of the magic and you wind up with the integral of (x^4+1)^1/2 over x^3. now with a substition you could make that into a form, sqrt(x2+1) over x2. That's what the book says to do. I'm a dork though and I don't want to use a 'form'. I mean I have to remember enough already, I'd rather just work though the problems. So I decide to tackle the bastard with some trigonometric substitution. I end up with sec^3 x over tan^2 x. I work that through into an integration by partial fractions problem, and blamo 1/1-u^2 + 1/u^2. Ok great on the u^-2, but now i've got another integration problem that I have to use a form for -- (1-u^2)^-1. So I tried to put sin x back into u. That winds up asking me to integrate sec x -- blam that one sucks. I've tried integration by parts and the third generation made we think I did something wrong. Anyone familiar with a proof of that and willing to give me any hints on the proper strategy? (on either the proof for (1-u^2)^-1 or sec x) So while writing this I got an idea that I could try substituting cos x and doing another substitution instead of going back one. I think i've done the homework problem for the integral of csc x. I'm going to do that but I have to get some housework done, go to work and study for physics exam. It's still going to bug me, I'd really be great for anyone and their ideas, below is the link to the work i've done in pdf if you want to see. The last line should be u^-2 it's a mistake. http://mypage.iu.edu/~nlcooper/math!.pdf thanks so much for anyone who can read through my buzzed mathmatical excursions. is differential stuff as fun? i'm looking forward to those and debating on changing my major from physics to math.