What is the result of integrating the expression x^3 - 4x + 1 dx?

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To find the integral of the expression (x^3 - 4x + 1) with respect to (x), we can apply the basic rules of integration to each term individually.

The integral of (x^3) is found using the power rule. According to the power rule, the integral of (x^n) is (\frac{1}{n+1}x^{n+1}). So, for (x^3), the integral is (\frac{1}{3+1}x^{4} = \frac{1}{4}x^4).

The integral of (-4x) can also be computed using the power rule. The integral of (x) is (\frac{1}{2}x^2), thus the integral of (-4x) is (-4 \cdot \frac{1}{2}x^2 = -2x^2).
Finally, the integral of the constant (1) is simply (x).

Combining all these results, we have:

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\int (x^3 - 4x + 1)