What is the integral of the expression (3x + 1)(2x - 3)?

To find the integral of the expression (3x + 1)(2x - 3), we begin by expanding the product:

(3x + 1)(2x - 3) can be expanded using the distributive property:

• Multiply 3x by each term in the second binomial:

3x * 2x = 6x^2 and 3x * -3 = -9x.

• Now, multiply 1 by each term in the second binomial:

1 * 2x = 2x and 1 * -3 = -3.

Combining these results gives:

6x^2 - 9x + 2x - 3 = 6x^2 - 7x - 3.

Now we need to integrate this resulting polynomial:

[

\int (6x^2 - 7x - 3) , dx.

]

We integrate each term separately:

• The integral of (6x^2) is (2x^3) (since ( \int x^n , dx = \frac{x^{n+1}}{n+1} + C)).

• The integral