Finding the area enclosed by Batman curve

Question

I was reading this thread:

Is this Batman equation for real?

and I wondered if the area bounded by the curve had a nice closed form.

The resulting integrals were slightly beyond me, so I thought I would ask you guys for help. Perhaps complex analysis will be useful.

Answer 1

http://www.wolframalpha.com/input/?i=batman+equation

If you go down to the section labelled area, they have the simplest form of the area of it.

$$\text{Area} = \frac{955}{48}-\frac{2}{7} (-3 \sqrt{10}+2 \sqrt{33}+7 \pi+3 \sqrt{10} \pi)+21 \cos^{-1}\left(\frac{3}{7}\right)+21 \cos^{-1}\left(\frac{4}{7}\right)$$