# Help with complicated integral, simplifying

1. Nov 12, 2008

### devanlevin

need to integrate the following equation from 1 to 3

$$\int$$$$\sqrt{4x^{6}+16x^{2}}$$

what i tried to do was call x^2, y for example then what i have is (4Y^3+16Y)^0.5
which i dont know how to integrate.
what else can i do, somehow need to play with the equation.

2. Nov 12, 2008

### Pere Callahan

If you let y=x^2 you have to replace x^2 by y and 2xdx by dy.

So I suggest you rewrite your integrand as

$$2x\sqrt{x^4+4}$$

Then applying the substitution, your integral becomes

$$\int_{1}^{9}{\sqrt{y^2+4}}$$

Can you finish from here?

3. Nov 12, 2008

### devanlevin

no, how do i integrate a sqr root with a squared number inside, the only format i have is for sqrt(ax+b)

4. Nov 12, 2008

### Pere Callahan

This is not so straightforward...are you familiar with the area hyperbolic functions (inverses of hyperbolic trigonometric functions)?

5. Nov 12, 2008

### devanlevin

no, any other ways

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