What is the integral of (3x-12)^2 ?

The integral of (3x-12)^2 is 3x^3-36x^2+144x+C

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integral of (3x-12)^2

\int (3 x - 12)^{2} d x

3 x^{3} - 36 x^{2} + 144 x + C

Solution steps

\int (3 x - 12)^{2} d x

Expand

(3 x - 12)^{2} : 9 x^{2} - 72 x + 144

= \int 9 x^{2} - 72 x + 144 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 9 x^{2} d x - \int 72 x d x + \int 144 d x

\int 9 x^{2} d x = 3 x^{3}

\int 72 x d x = 36 x^{2}

\int 144 d x = 144 x

= 3 x^{3} - 36 x^{2} + 144 x

Add a constant to the solution

= 3 x^{3} - 36 x^{2} + 144 x + C

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What is the integral of (3x-12)^2 ?
The integral of (3x-12)^2 is 3x^3-36x^2+144x+C