Arc Length Problem?

Question

Here's the Problem:

Find the arc length of y = [(x^3)/6] + [1/(2x)] on [0.5,2]

I struggling with the algebra on this problem, can anyone be kind enough to help?

Note: I cannot use any form of integration techniques other than U-Subsitution or just taking the antiderivative. Cannot use trig sub, integration by parts, or partial fractions decomposition. These are in the next chapter. Thank You

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Answer 1 · 2018-03-27T11:04:42

#33/16#

Given #y = x^3/6+1/(2x)# we have

#y'=x^2/2-1/(2x^2)# and

#ds = sqrt(1+(dy/dx)^2)dx = 1/2(sqrt(2 + 1/x^4 + x^4)) dx= 1/2(x^2+1/x^2)dx#

and

#s = int_(1/2)^2 1/2(x^2+1/x^2)dx = 33/16#