What is the integral of (x+5)(x-11) ?

The integral of (x+5)(x-11) is (x^3)/3-3x^2-55x+C

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integral of (x+5)(x-11)

\int (x + 5) (x - 11) d x

\frac{x ^{3}}{3} - 3 x^{2} - 55 x + C

Solution steps

\int (x + 5) (x - 11) d x

Expand

(x + 5) (x - 11) : x^{2} - 6 x - 55

= \int x^{2} - 6 x - 55 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 6 x d x - \int 55 d x

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

\int 6 x d x = 3 x^{2}

\int 55 d x = 55 x

= \frac{x ^{3}}{3} - 3 x^{2} - 55 x

Add a constant to the solution

= \frac{x ^{3}}{3} - 3 x^{2} - 55 x + C

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What is the integral of (x+5)(x-11) ?
The integral of (x+5)(x-11) is (x^3)/3-3x^2-55x+C