What is the integral of (8x-12)(4x^2-12x) ?

The integral of (8x-12)(4x^2-12x) is 8x^4-48x^3+72x^2+C

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integral of (8x-12)(4x^2-12x)

\int (8 x - 12) (4 x^{2} - 12 x) d x

8 x^{4} - 48 x^{3} + 72 x^{2} + C

Solution steps

\int (8 x - 12) (4 x^{2} - 12 x) d x

Expand

(8 x - 12) (4 x^{2} - 12 x) : 32 x^{3} - 144 x^{2} + 144 x

= \int 32 x^{3} - 144 x^{2} + 144 x 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 32 x^{3} d x - \int 144 x^{2} d x + \int 144 x d x

\int 32 x^{3} d x = 8 x^{4}

\int 144 x^{2} d x = 48 x^{3}

\int 144 x d x = 72 x^{2}

= 8 x^{4} - 48 x^{3} + 72 x^{2}

Add a constant to the solution

= 8 x^{4} - 48 x^{3} + 72 x^{2} + C

7 sin (x)

y = ln (\frac{x + 1}{x - 1})

\frac{d y}{d t} = 2 t y^{2} + 3 y^{2}

x \to + 0 + lim ((7 x)^{x})

\int_{- \infty}^{\infty} x e^{x^{2}} d x

What is the integral of (8x-12)(4x^2-12x) ?
The integral of (8x-12)(4x^2-12x) is 8x^4-48x^3+72x^2+C