Last question of the day. Been working on math for about 8 hours now....

Consider the curve r=(e^(2t)*cos(−2t),e^(2t)*sin(−2t),e^(2t)).

Compute the arclength function s(t): (with initial point t=0).

Now the derivatives are

r'(t)= (2e^2t[cos(2t)-sin(2t)] , -2e^(2t)[sin(2t)+cos(2t)], 2e^2t)

I know that s(t)= Integral from 0 to t of |r'(t)|

Can someone show me the work of finding |r'(t)|. It should be simple but no matter how many times I work it, I keep getting the wrong answers.

|r'(t)|= sqrt(4e^(4t)*(1-sin(4t))+4e^(4t)*(1+sin(4t))+4e^(4t)

This is the simplified version, don't know if it's anywhere near correct, because I get a different answer every time I work the problem, and it's always the wrong answer. :\ Getting frustrated.