Arc length of a curve represented by vector function

I'm having some trouble doing this question where i'm supposed to find the arc length of a curve represented by a vector function.

Question is: Find the arc length of the curve.

$\displaystyle r(t) = (\sqrt(2)*t) i + (e^t)j + 1/(e^t)k$ over the interval $\displaystyle 0<=t<=1$

So since arc length = int(0,1)[|r`(t)|] i calculate r`(t):

$\displaystyle r`(t) = \sqrt(2)i + (e^t)j + -1/(e^t)k$

and

$\displaystyle |r`(t)| = \sqrt(2 + (e^t)^2 + -1/(e^t)^2 )$

and this is where i get stuck. I must have to plug something into |r`(t)| equation above for t to calculate |r`(t)| and then plug it into the arc length equation. How am i supposed to integrate |r`(t)| as it is shown in the above form?