g = 1 + Sin[y]\(	yl = 1 - r^2\)al = 1 + r^2 - 2*r*Cos[th - y]

1/(2*Pi)*Integrate[yl/al*g, {y, 0, 2*Pi}]

Simplify[%]

g2 = 2 + Sin[y]/2 - Cos[y]/10 + (Sin[y])^2 + Cos[4*y]

Integrate[yl/al*g2, {y, 0, 2*Pi}]

Simplify[%]