The power rule states that the integral of x^n dx is (1/(n+1))x^(n+1). Applying this rule to the first term, 3x, we get (3/2)x^2. Applying this rule to the second term, -x^3, we get -(1/4)x^4. So, the integral becomes:
$$\int_{0}^{1}\left(3 x-x^{3}\right) d x =
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