That was a ton of help! Thank you!! (Clapping) I still ran into a rough spot...and I'll show you where it got messy, so I'm not completely sure that my answer is 100% right.

so, starting from where o_O left off, the integral of r*sec(theta)*tan(theta)d(theta)/sqrt((r^2)(sec^2(theta)-1) = the integral of (r*sec(theta)*tan(theta)d(theta))/sqrt((r^2)-tan^2(theta) = the integral of (r*sec(theta)*tan(theta)d(theta))/(r*tan(theta)) = the integral of sec(theta)d(theta)

at which point I googled some

help, which gave me a very detailed solution, that I probably wouldn't have thought of on my own.

getting back to my eventual answer, I end up with ln|sec(theta) + tan(theta)| + C. But then I need to convert back to x and r.

I find that theta = arcsec(x/r), through the first trig substitution that Chris L T521 gave me.

substituting back in, gives me ln|(x/r) + tan(arcsec(x/r)|+C

I'm not sure that this is the simpliest form?

Whew that was long..I really need to figure out how to work these math symbols so it doesn't look so messy....Thanks again!