find integral sqrt(1+(cosx)^2)*sin2x*cos2x. solve the same

We know that cos^2x= (1+cos2x)/2

So put cos2x=y

After taking constants out, we ll have to integrate

y√(3+y)dy

This is particularly easy and you simply have to write it as (3+y)^(3/2)-3(3+y)^(1/2). Now substitute 3+y=z and you are done