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

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

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

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

3 x^{3} - x + C

Solution steps

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

Expand

(3 x - 1) (3 x + 1) : 9 x^{2} - 1

= \int 9 x^{2} - 1 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 1 d x

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

\int 1 d x = x

= 3 x^{3} - x

Add a constant to the solution

= 3 x^{3} - x + C

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