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

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

• A. (1/3)x^3 + (3/2)x^2 + 2x + C
• B. (1/2)x^2 + (3/3)x^3 + 2 + C
• C. (1/4)x^4 + (3/3)x^3 + 2 + C
• D. (1/5)x^5 + (3/2)x^2 + 2 + C

Answer: (A)

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

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:

[

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