What is the integral of 3(x-3)(x+1) ?

The integral of 3(x-3)(x+1) is x^3-3x^2-9x+C

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integral of 3(x-3)(x+1)

\int 3 (x - 3) (x + 1) d x

x^{3} - 3 x^{2} - 9 x + C

Solution steps

\int 3 (x - 3) (x + 1) d x

Take the constant out:

\int a \cdot f (x) d x = a \cdot \int f (x) d x

= 3 \cdot \int (x - 3) (x + 1) d x

Expand

(x - 3) (x + 1) : x^{2} - 2 x - 3

= 3 \cdot \int x^{2} - 2 x - 3 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

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

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

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

\int 3 d x = 3 x

= 3 (\frac{x ^{3}}{3} - x^{2} - 3 x)

Simplify

3 (\frac{x ^{3}}{3} - x^{2} - 3 x) : x^{3} - 3 x^{2} - 9 x

= x^{3} - 3 x^{2} - 9 x

Add a constant to the solution

= x^{3} - 3 x^{2} - 9 x + C

- 3

x = y^{2} - 8 y, x = 3 y - y^{2}

\int 10 x + 6 d x

y^{^{''}} - (\frac{3}{x}) y^{^{'}} - (\frac{4}{x ^{2}}) y = 0

\int (\frac{( x + 1 ) ( x - 1 )}{x}) d x

What is the integral of 3(x-3)(x+1) ?
The integral of 3(x-3)(x+1) is x^3-3x^2-9x+C