How do I Integrate \sqrt{1+x^4+2x^2}?

[miglo]

Homework Statement

$$y=\frac{1}{3}\left(x^2+2\right)^{3/2}$$

Homework Equations

$$\int_{a}^{b}\sqrt{1+\left(\frac{dy}{dx}\right)^{2}}dx$$

The Attempt at a Solution

$$\frac{dy}{dx}=x\sqrt{x^2+2}$$
$$\int_{0}^{3}\sqrt{1+\left(x\sqrt{x^2+2}\right)^{2}}dx=\int_{0}^{3}\sqrt{1+x^4+2x^2}dx$$
I'm stuck with that integral, not sure what the antiderivative for that function would be
Any hints at the next step would be greatly appreciated.

 

[Char. Limit]

Here's a hint: x⁴+2x²+1 = (x²+1)²

 

[miglo]

Wow I can't believe i didn't see that.
I tried Wolfram Alpha earlier and they used a substitution but i couldn't follow their steps so i decided to consult the Physics Forums.
Thanks Char. Limit.