What is the integral of (x-5)(x+3) ?

The integral of (x-5)(x+3) is (x^3)/3-x^2-15x+C

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integral of (x-5)(x+3)

\int (x - 5) (x + 3) d x

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

Solution steps

\int (x - 5) (x + 3) d x

Expand

(x - 5) (x + 3) : x^{2} - 2 x - 15

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

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

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

\int 15 d x = 15 x

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

Add a constant to the solution

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

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What is the integral of (x-5)(x+3) ?
The integral of (x-5)(x+3) is (x^3)/3-x^2-15x+C