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**rain21** Find the length of the curve $\displaystyle r(t)=<ln(5t), 2t , t^2> , 2\leq t \leq 3 $

I am still trying to figure out how to use latex so forgive me if it is a little messed up. the integral is supposed to be from 2 to 3

this is my solution, so far...

$\displaystyle r'(t) = <\frac{1}{t} , 2 , 2t > $

$\displaystyle |r'(t)| = \sqrt{\frac{1}{t^2}+ 4 + 4t^2} $

$\displaystyle _2\int^3 |r'(t)|dt = _2\int^3 |r'(t)| dt = _2\int^3 \sqrt{\frac{1}{t^2}+ 4 + 4t^2} dt $

I am a bit rusty on integration and cannot get the correct answer from this point. I was thinking of using u substitution but cannot figure out how to do it correctly.