What is the integral of x^2 + 3x + 2 dx?

To find the integral of the function ( x^2 + 3x + 2 ), we use the power rule of integration, which states that the integral of ( x^n ) is ( \frac{x^{n+1}}{n+1} + C ) for any constant ( n \neq -1 ).

Applying this rule to each term in the polynomial:

1. For the term ( x^2 ):

• The integral is ( \frac{x^{2+1}}{2+1} = \frac{x^3}{3} ).

2. For the term ( 3x ):

• The integral is ( 3 \cdot \frac{x^{1+1}}{1+1} = 3 \cdot \frac{x^2}{2} = \frac{3}{2}x^2 ).

3. For the constant term ( 2 ):

• The integral is ( 2x ) because the integral of a constant ( a ) is ( ax ).

Putting it all together, we have:

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\int (x^2 + 3x + 2) , dx = \frac