What is the integral of (5x+2)(x-4) ?

The integral of (5x+2)(x-4) is (5x^3)/3-9x^2-8x+C

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integral of (5x+2)(x-4)

\int (5 x + 2) (x - 4) d x

\frac{5 x ^{3}}{3} - 9 x^{2} - 8 x + C

Solution steps

\int (5 x + 2) (x - 4) d x

Expand

(5 x + 2) (x - 4) : 5 x^{2} - 18 x - 8

= \int 5 x^{2} - 18 x - 8 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 5 x^{2} d x - \int 18 x d x - \int 8 d x

\int 5 x^{2} d x = \frac{5 x ^{3}}{3}

\int 18 x d x = 9 x^{2}

\int 8 d x = 8 x

= \frac{5 x ^{3}}{3} - 9 x^{2} - 8 x

Add a constant to the solution

= \frac{5 x ^{3}}{3} - 9 x^{2} - 8 x + C

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What is the integral of (5x+2)(x-4) ?
The integral of (5x+2)(x-4) is (5x^3)/3-9x^2-8x+C