Find the integral of (2x^3 - 6x + 3) dx.

To find the integral of the function (2x^3 - 6x + 3), we apply the power rule of integration to each term individually. The power rule states that the integral of (x^n) is (\frac{x^{n+1}}{n+1} + C), where (C) is the constant of integration.

1. For the term (2x^3):

• The integral is (\int 2x^3 , dx = 2 \cdot \frac{x^{4}}{4} = \frac{1}{2}x^4).

2. For the term (-6x):

• The integral is (\int -6x , dx = -6 \cdot \frac{x^{2}}{2} = -3x^2).

3. For the constant term (3):

• The integral is (\int 3 , dx = 3x).

Combining these results gives:

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\int (2x^3 - 6x + 3) , dx = \frac{1}{2}x^4 - 3