(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

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

2. Relevant equations

L = ∫|r'(t)|

3. 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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# Integration of e

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