Evaluate: ∫cosx-sinxcosx+sinx(2+2sin2x)dx
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∫cosx+sinxcosx−sinx⋅(2+2sin2xdx)⇒2×∫(cosx+sinx)cosx−sinx(sin2x+cos2xsin2x)dx⇒2∫cosx+sinxcosx−sinx×[sinx+cosx]2dx⇒2∫(cosx−sinx)(cosx+sinx)dx⇒2∫cos2x−sin2xdx⇒2×∫cos2xdx⇒2×2sin2x+c⇒sin2x+c
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