Hey, I have an area problem that looks like it should simplify, but the integral I have set up does not seem to be solvable with my current skill set. If anyone has a second to look over my set up to see where I went wrong, I would be extremely appreciative!

So using the SA formula: $\displaystyle r = y = tan(x)$ and $\displaystyle \frac{dy}{dx}=sec^2(x)$.

So $\displaystyle \sqrt{1+(\frac{dy}{dx})^2} = \sqrt{1+sec^4(x)}$.

This gives rise to the SA integral:

$\displaystyle S = 2\pi \int_{0}^{\frac{\pi}{4}} tan(x) \sqrt{1+sec^4(x)} dx$

I cannot figure out how to solve this integral, any hints? Just a hint as well please, not looking for a complete solution.

Thanks