Now, as you found:
So, taking the square root and our final integral becomes:
I need to find the length of the curve y=(1/2)x^2 - (1/4)lnx between x=1 and x=8.
I derived it and squared it and added one to it so now I'm left with the integral from 1 to 8 of sqrt (x^2 + (1/2) + 1/16x^2) dx. How do I integrate this?