Find the length of the curve r(t)=  from t=1 to t=e Find the length of the curve r(t)= $<t^2,2t,lnt> $
from t=1 to t=e
i know that Length= $\int$ length of r'(t) dt
Therefore, L= $\int _1^e\sqrt{4t^2+4+\frac{1}{t^2}}dt\$$
but i'm having trouble with solving this integral? i would think of u sub but having trouble what to set u equal to if that's even the approach i should be taking?
i've also tried taking out a $t^2$ to have a $t$ outside of the square root but still get lost

We have,
$$
4t^2+4+\frac1{t^2}=(2t+\frac1t)^2
$$
