Math Help - Stumped by an Integral

1. Stumped by an Integral

Can anyone solve this?

$\int_0^5\sqrt{1+(3t^2-12t+9)^2}dt$

I'm not sure where to begin on this one. Any suggestions? It seems like one of those functions that you just can't evaluate by hand. However, I'm not very clever when integrating, so maybe it's just me

Would it be easier to do a Riemann sum?

2. I don't think this integral can be calculated using elementary methods ... there may be a clever trig or algebraic substitution, but I'm not seeing it.

my TI-89 sez 29.0708...

3. http://integrals.wolfram.com/index.jsp?expr=sqrt(9+(x^2-4+x%2B3)^2%2B1)&random=false

Mathematica disagrees with your simple substitution

4. Originally Posted by Silent Soliloquy
http://integrals.wolfram.com/index.jsp?expr=sqrt(9+(x^2-4+x%2B3)^2%2B1)&random=false

Mathematica disagrees with your simple substitution
That's not what I wrote originally actually, but I was completely wrong nonetheless. My trig idea doesn't work with the 4th power. Even if I had factored correctly I didn't account for the problem of dtheta, which added more than I said originally. Yes, I messed up.

5. It seems like Simpsons rule is going to be my best choice.