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\[\int\limits_{1/2}^{1} dx/ x ^{2}\sqrt{x ^{2} + 4}\]

put x=2tan u

okay im left with \[1/4\int\limits_{1/2}^{1} \sec \theta/\sec ^{2}\theta -1 \]

yeah thats what i was trying to do. okay let me try it with sines and cosines

still a bit confused as to what to do with the term thats squared

Yah I did that upside down :) woops lol

i think its cos over sin squared

yah good call XD whatever is on the bottom is your `u` :3

okay thanks a lot!