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

The integral of x(x^2-12) is (x^4)/4-6x^2+C

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integral of x(x^2-12)

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

\frac{x ^{4}}{4} - 6 x^{2} + C

Solution steps

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

Expand

x (x^{2} - 12) : x^{3} - 12 x

= \int x^{3} - 12 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 x^{3} d x - \int 12 x d x

\int x^{3} d x = \frac{x ^{4}}{4}

\int 12 x d x = 6 x^{2}

= \frac{x ^{4}}{4} - 6 x^{2}

Add a constant to the solution

= \frac{x ^{4}}{4} - 6 x^{2} + C

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