What is the integral of (x+2)(x-6) ?

The integral of (x+2)(x-6) is (x^3)/3-2x^2-12x+C

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integral of (x+2)(x-6)

\int (x + 2) (x - 6) d x

\frac{x ^{3}}{3} - 2 x^{2} - 12 x + C

Solution steps

\int (x + 2) (x - 6) d x

Expand

(x + 2) (x - 6) : x^{2} - 4 x - 12

= \int x^{2} - 4 x - 12 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 4 x d x - \int 12 d x

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

\int 4 x d x = 2 x^{2}

\int 12 d x = 12 x

= \frac{x ^{3}}{3} - 2 x^{2} - 12 x

Add a constant to the solution

= \frac{x ^{3}}{3} - 2 x^{2} - 12 x + C

9 y^{^{''}} - 6 y^{^{'}} + 15 y = 0

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

\frac{d}{d x} (\frac{x + 1}{2 x})

What is the integral of (x+2)(x-6) ?
The integral of (x+2)(x-6) is (x^3)/3-2x^2-12x+C