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

The integral of (x-2)(2x+3) is (2x^3)/3-(x^2)/2-6x+C

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

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

\frac{2 x ^{3}}{3} - \frac{x ^{2}}{2} - 6 x + C

Solution steps

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

Expand

(x - 2) (2 x + 3) : 2 x^{2} - x - 6

= \int 2 x^{2} - x - 6 d x

Apply the Sum Rule:

\int f (x) \pm g (x) d x = \int f (x) d x \pm \int g (x) d x

= \int 2 x^{2} d x - \int x d x - \int 6 d x

\int 2 x^{2} d x = \frac{2 x ^{3}}{3}

\int x d x = \frac{x ^{2}}{2}

\int 6 d x = 6 x

= \frac{2 x ^{3}}{3} - \frac{x ^{2}}{2} - 6 x

Add a constant to the solution

= \frac{2 x ^{3}}{3} - \frac{x ^{2}}{2} - 6 x + C

x \frac{d y}{d x} = y ln (x y)

\frac{\partial}{\partial x} (sin (y) e^{x})

n = 0 \sum \infty \frac{3 ^{n}}{n}

\int_{0}^{2} - 3 x^{3} x^{2} + 4 d x

\frac{16}{s ^{2} + 3 s + 16}

What is the integral of (x-2)(2x+3) ?
The integral of (x-2)(2x+3) is (2x^3)/3-(x^2)/2-6x+C