Question

Having trouble integrating something with a few u-substitutions. I'm just getting lost part of the way in. Posted below in a minute.

Answer 1

\[\int\limits_{}^{}\frac{ 1 }{ (2x-1)\sqrt{(2x-1)^{2}-4} }dx;\]\[u = (2x-1), du = 2dx\]\[\int\limits_{}^{}\frac{ 1 }{ (2x-1)\sqrt{(2x-1)^{2}-4} }dx=\int\limits_{}^{}\frac{ 1 }{ 2 }\frac{ 1 }{ u \sqrt{u ^{2}-4} };\]\[u = 2\sec(s), du = 2\sec(s)\tan(s)\] Here I know I'm supposed to make these substitutions, but I'm having a hell of a difficult time doing so.

Answer 2

Nevermind, figured it out, I was supposed to utilize a trig identity I'm not familiar with.

Answer 3

was it an inverse trig ident?

Answer 4

Yeah, I was supposed to use sec^(-1)x, but I might actually be a little more confused now, lol. This is a rather annoying integral.