How do I integrate sin^2(x)?

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First, remember the compound angle formula for cosine:

cos(2x)=cos^2(x)-sin^2(x).  Now use the identity sin^2(x)+cos^2(x)=1 to give:


Rearranging this so we have sin^2(x)=1/2(1-cos(2x))

Replace this with the original integration and use the chain rule to get:


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