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

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

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

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

\frac{x ^{3}}{3} - 4 x + C

Solution steps

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

Expand

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

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

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

\int 4 d x = 4 x

= \frac{x ^{3}}{3} - 4 x

Add a constant to the solution

= \frac{x ^{3}}{3} - 4 x + C

f (x) = 4 tan (x), at x = \frac{π}{6}

\frac{d}{d x} (ln (x^{3}) + 2 x)

\frac{d}{d x} (cos (x) sin^{2} (x))

y^{^{'}} = - 4 x y

\frac{\partial}{\partial x} (\frac{x y}{x + 7})