How to find: $\int^{2\pi}_0 (1+\cos(x))\cos(x)(-\sin^2(x)+\cos(x)+\cos^2(x))~dx$? How to find: $$\int^{2\pi}_0 (1+\cos(x))\cos(x)(-\sin^2(x)+\cos(x)+\cos^2(x))~dx$$
I tried multiplying it all out but I just ended up in a real mess and I'm wondering if there is something I'm missing.

try to show that the integrand is equivalent to $$\frac{1}{4} (7 \cos (x)+4 \cos (2 x)+\cos (3 x)+4)$$
