Recognize integral type: Step 1: Recognize the integral type.We have the integral of a trigonometric function, which suggests a potential substitution. The integral is ∫−6π3πcos2x−sinxdx. Recognizing that dxd(tanx)=sec2x, we can use a substitution.
Perform substitution: Step 2: Perform the substitution.Let u=tanx, then du=sec2xdx. Since sec2x=1/cos2x, we can rewrite dx as dx=cos2xdu. Substituting into the integral, we get:∫cos2x−sinxdx=∫−sinxduThis is incorrect because we didn't adjust the sinx term properly for the substitution.
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