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, e5t, e-5t>
L = ∫|r'(t)|
The Attempt at a Solution
r'(t) = √((5√(2))2+(5e5t)2+(-5e-5t)2)
|r'(t)| = 5√(2+e10t+e-10t)
Now this is where I get confused.
∫(5√(2+e10t+e-10t)) = ((e10t-1)*√(2+e10t+e-10t))/(e10t+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.