Calculating Arc Length of a Vector Function

[rwisz]

Homework Statement

Find Arc Length:
r(t)=t^3 i+tj+(1/2)$$\sqrt{6}$$t^2k 1$$\leq$$t$$\leq$$3

Homework Equations

The arc length formula:
integrate: sqrt((dx/dt)^2+(dy/dt)^2+(dz/dt)^2) dt

The Attempt at a Solution

I can find the derivative and plug into the formula, it's just the simplification that is absolutely stumping me. I haven't done this for a long time, which is always why my TeX is horribly put together.

Any help is greatly appreciated. I've gotten to here so far:

$$\int_1^3 \! \sqrt{9t^4+1+6t^2} \, dt.$$

 

[Dick]

The expression under the square root is a perfect square. Factor it!

 

[rwisz]

Thank you. I'm sorry for the nonsensical post, I guess I was way too tired to not have that jump out at me.

Again, thank you.