Integrate sqrt(1+(1\sqrt(x)))^2

Good morning,

I left off on this problem yesterday. I am given:

Find the surface area by revolving around the x-axis:

$\displaystyle f(x) = 2\sqrt{x}$ for $\displaystyle 1\leq x \leq4$

So far I have the following:

$\displaystyle

f'(x) = \frac{1}{\sqrt{x}}

$

$\displaystyle \sqrt{1+(\frac{1}{\sqrt{x}})^2} = \sqrt{\frac{x+1}{x}}$

So...

$\displaystyle

L = \int_{1}^{4}{\sqrt{\frac{x+1}{x}} dx

$

And... I'm stuck.

I don't now why roots are giving me so much trouble lately. Is there something that I have forgotten or seem to be missing? I don't recall roots being this problematic.