Help with complicated integral, simplifying

[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 don't know how to integrate.
what else can i do, somehow need to play with the equation.

 

[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

<br /> 2x\sqrt{x^4+4}<br />

Then applying the substitution, your integral becomes

<br /> \int_{1}^{9}{\sqrt{y^2+4}}<br />

Can you finish from here?

 

[devanlevin]

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

 

[Pere Callahan]

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

 

[devanlevin]

no, any other ways