1. The problem statement, all variables and given/known data Find the arc length of r(t)= <tsin(t), tcost(t), 3t> from 0 to t to 2pi (inclusive) 2. Relevant equations Integral from 0 to 2pi of the magnitude of r'(t) dt 3. The attempt at a solution 1. Must find the derivative of the function. Using the product rule a few times, the derivative becomes <tcos(t)+sin(t), -tsin(t)+cos(t), 3> 2. Now take the magnitude Well, this is a bit lengthy, but it simplifies pretty nice with the double angle trig identity. (I hope what I did is correct, please check my work in this step. (tcos(t)+sin(t))^2 = t^2cos^2t+2tsin(t)*cos(t)+sin^2t Simplifies to: t^2cos^2t+tsin(2t)+sin^2t (-tsin(t)+cos(t))^2 = t^2sin^2t+(-2tsin(t)*cos*(t))+cos^2t simplifies to: t^2sin^2t-tsin(2t)+cos^2t 3^2 = 9 So, when we add everything the double angles cancel out. The cos^2t+sin^2t is equal to 1. We factor a t^2 out of the t^2cos^2t and t^2sin^2t equations and this becomes t^2*1. We are left with 9+1+t^2 t^2+10, beautiful! 3. Integrate from 0 to 2pi the square root of (t^2+10) dt Well, here's where I am stuck. I feel like I've done everything properly up to this point. But this integral cannot be taken easily (at least with calc 3 tools). Did I do something wrong? Any hints on the integral?