What is the integral of (3x-4)(2x+3) ?

The integral of (3x-4)(2x+3) is 2x^3-4x^2+(9x^2)/2-12x+C

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integral of (3x-4)(2x+3)

\int (3 x - 4) (2 x + 3) d x

2 x^{3} - 4 x^{2} + \frac{9 x ^{2}}{2} - 12 x + C

Solution steps

\int (3 x - 4) (2 x + 3) d x

Apply Integration By Parts

= 3 x^{3} - 8 x^{2} + \frac{9 x ^{2}}{2} - 12 x - \int 3 x^{2} - 8 x d x

\int 3 x^{2} - 8 x d x = x^{3} - 4 x^{2}

= 3 x^{3} - 8 x^{2} + \frac{9 x ^{2}}{2} - 12 x - (x^{3} - 4 x^{2})

Simplify

3 x^{3} - 8 x^{2} + \frac{9 x ^{2}}{2} - 12 x - (x^{3} - 4 x^{2}) : 2 x^{3} - 4 x^{2} + \frac{9 x ^{2}}{2} - 12 x

= 2 x^{3} - 4 x^{2} + \frac{9 x ^{2}}{2} - 12 x

Add a constant to the solution

= 2 x^{3} - 4 x^{2} + \frac{9 x ^{2}}{2} - 12 x + C

What is the integral of (3x-4)(2x+3) ?
The integral of (3x-4)(2x+3) is 2x^3-4x^2+(9x^2)/2-12x+C