The Attempt at a Solution
I know the answer, and i know how to get there using:
But why cant i use the chain rule? Can i?
You must also consider the variable of integration. Since you've made a substitution [itex] u [/itex], you want to integrate with respect to [itex] u [/itex], and as HallsofIvy said, this is moot because of the chain rule.u=cosx
∫(cos2x)dx = ∫(u2)dx = (1/3)u3/u' + C = (1/3)cosx3/(cosx)' + C = (1/3)cosx3/(-sinx) + C
chain rule reversed?