What is the integral of (x+4)(x-6) ?

The integral of (x+4)(x-6) is (x^3)/3-x^2-24x+C

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integral of (x+4)(x-6)

\int (x + 4) (x - 6) d x

\frac{x ^{3}}{3} - x^{2} - 24 x + C

Solution steps

\int (x + 4) (x - 6) d x

Expand

(x + 4) (x - 6) : x^{2} - 2 x - 24

= \int x^{2} - 2 x - 24 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 24 d x

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

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

\int 24 d x = 24 x

= \frac{x ^{3}}{3} - x^{2} - 24 x

Add a constant to the solution

= \frac{x ^{3}}{3} - x^{2} - 24 x + C

\frac{d}{d x} (\frac{x ^{2}}{arccos ( x ^{2} )})

g (t) = sin (2 t + 5)

\int \frac{x ^{2}}{( 25 - x ^{2} ) ^{\frac{3}{2}}} d x

2 t + 1

x = 6 y^{3}, x = 21 y^{2}

What is the integral of (x+4)(x-6) ?
The integral of (x+4)(x-6) is (x^3)/3-x^2-24x+C