calculus

Find the length of the arc formed by
y = (1/8)(4x^2-2ln(x)) from x=4 to x=8.

I found the derivative of the function and got y'= x-(1/4x)

Where I'm lost now is after plugging it into the arc length equation: integral of sqrt(1+(x-(1/4x))^2). Squaring the derivative yields me sqrt(1+x^2+1/16x-1/2). Help please.

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  1. I got sqrt [ 1 + x^2 -(1/2) + 1/(16x^2) ]
    which is
    sqrt [ x^2 + (1/2) +1/(16x^2) ]
    BUT
    x^2 + (1/2) + 1/(16x^2) = [x+ 1/(4x)]^2
    ok ?

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    posted by Damon
  2. Oh yes, sorry, I merely had a typo. I had the same result as you. What I'm confused about is what to do from that point on.

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  3. well, the sqrt of that is just
    x + (1/4)(1/x)
    integral of that is
    (1/2) x^2 + (1/4) ln x

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    posted by Damon

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