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:
cos(2x)=(1-sin^2(x))-sin^2(x)=1-2sin^2(x)
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:
1/2(x-1/2sin(2x))+c
