The standard integral formula is ∫sin(ax) dx = -(1/a)cos(ax) + C. In this case, a = 2. Therefore, ∫sin(2x) dx = -(1/2)cos(2x) + C. Option 2 is incorrect because the integral of the sine function is negative cosine. Option 3 is a common mistake where the student multiplies by the constant (as in differentiation) instead of dividing. Option 4 neglects the coefficient introduced by the substitution method (chain rule in reverse).