Find area of limacon.

Well I cant seem to get the latex to work for the integral that I set up so here it is rougly.

Upper limit Pi

Lower limit 0

1/2 int (4+2cos theta)^2 dtheta

by symmetry I multiply by 2 which gets rid of the 1/2 outside

Then

foiling

int (16) + int (16 cos theta) + int (4 cos^2theta) dtheta

16 theta - 16 sin theta + 4 int 1 + cos(2theta)/2 dtheta

Am I going the right way with this integral? If not where am I going wrong?

Thanks