MHB Calculating Curve Length: A Shortcut for Solving Complex Equations?

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To find the length of the curve defined by y = (x^5)/6 - (ln x)/4 from x = 2 to x = 4, the integral to evaluate is ∫ from 2 to 4 of √(1 + (5x^4/6 - 1/(4x))^2) dx. Users are encouraged to share their progress to receive targeted assistance. Numeric integration techniques may be necessary for this problem, and using a calculator could expedite the solution. Engaging in these methods can help simplify the process of solving complex equations.
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Hi everyone, I have an exercise I haven't solved yet, please help me.
Find the length of the curve: $$y = \frac{{x}^{5}}{6} - \frac{lnx}{4}, 2 \le x \le 4$$.
 
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Hello and welcome to MHB, mathforsure! :D

We ask that our users show their progress (work thus far or thoughts on how to begin) when posting questions. This way our helpers can see where you are stuck or may be going astray and will be able to post the best help possible without potentially making a suggestion which you have already tried, which would waste your time and that of the helper.

Can you post what you have done so far?
 
My progress, the last step is find the integral:
$$\int_{2}^{4}\sqrt{1 + (\frac{5x^{4}}{6} - \frac{1}{4x})^{2}}\,dx$$
 
I could be wrong, but it appears to me that you will need to use some sort of numeric integration technique. (Worried)
 
I think the fastest solution is using calculator (Wink)
 
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