What is the integral of (x-4)(-2x+7) ?

The integral of (x-4)(-2x+7) is -(2x^3)/3+(15x^2)/2-28x+C

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integral of (x-4)(-2x+7)

\int (x - 4) (- 2 x + 7) d x

- \frac{2 x ^{3}}{3} + \frac{15 x ^{2}}{2} - 28 x + C

Solution steps

\int (x - 4) (- 2 x + 7) d x

Expand

(x - 4) (- 2 x + 7) : - 2 x^{2} + 15 x - 28

= \int - 2 x^{2} + 15 x - 28 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 15 x d x - \int 28 d x

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

\int 15 x d x = \frac{15 x ^{2}}{2}

\int 28 d x = 28 x

= - \frac{2 x ^{3}}{3} + \frac{15 x ^{2}}{2} - 28 x

Add a constant to the solution

= - \frac{2 x ^{3}}{3} + \frac{15 x ^{2}}{2} - 28 x + C

What is the integral of (x-4)(-2x+7) ?
The integral of (x-4)(-2x+7) is -(2x^3)/3+(15x^2)/2-28x+C