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## Homework Statement

I have the problem and answer, I'm just confused on the last step, but I'll put down everything anyways.

Find the arclength of the curve r(t) = <5√(2)t, e

^{5t}, e

^{-5t}>

0≤t≤1

## Homework Equations

L = ∫|r'(t)|

## The Attempt at a Solution

r'(t) = √((5√(2))

^{2}+(5e

^{5t})

^{2}+(-5e

^{-5t})

^{2})

|r'(t)| = 5√(2+e

^{10t}+e

^{-10t})

Now this is where I get confused.

∫(5√(2+e

^{10t}+e

^{-10t})) = ((e

^{10t}-1)*√(2+e

^{10t}+e

^{-10t}))/(e

^{10t}+1)

I just don't understand how to integrate my answer to get that. If someone could just go through the steps that'd be great. Thanks!

Then obviously sub in for 1 and 0, getting 148.4064 which is correct so I know that the integration is correctly done.

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