Hello Se,
First of all I think you probably mean the integral of
P(1,n,cos(theta))*cos(theta)^2
which is what makes sense when trig functions come into it. This issue has caused a lot of back and forth on your other posted question. Also, this integrand would usually be multiplied by sin(theta) since sin(theta)* dtheta is part of the volume element in spherical coordinates. Are you looking for this integral from ) 0 to pi?
