What is the antiderivative of ##sin^2(x)##?

##= 1/2[x – 1/2sin2x] + C##

We’re going to use the trig identity

##cos2theta = 1 -2sin^2theta##

##implies sin^2x = 1/2(1 – cos2x)##

So ##int sin^2xdx = 1/2int(1-cos2x)dx##

##= 1/2[x – 1/2sin2x] + C##

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