Find the exact length of the curve analytically by antidifferentiation. You will need to simplify the integrand algebraically before finding an antiderivative.

$\displaystyle x= \frac{y^3}{3} + \frac{1}{4y}$

from y=1 to y= 3

Hint:$\displaystyle 1 + (\frac{dy}{dx})^2)$ is a perfect square.

I don't see the perfect square.

Thanks.