What is the integral of (2x+1)(2x-1) ?

The integral of (2x+1)(2x-1) is (4x^3)/3-x+C

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integral of (2x+1)(2x-1)

\int (2 x + 1) (2 x - 1) d x

\frac{4 x ^{3}}{3} - x + C

Solution steps

\int (2 x + 1) (2 x - 1) d x

Expand

(2 x + 1) (2 x - 1) : 4 x^{2} - 1

= \int 4 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 4 x^{2} d x - \int 1 d x

\int 4 x^{2} d x = \frac{4 x ^{3}}{3}

\int 1 d x = x

= \frac{4 x ^{3}}{3} - x

Add a constant to the solution

= \frac{4 x ^{3}}{3} - x + C

What is the integral of (2x+1)(2x-1) ?
The integral of (2x+1)(2x-1) is (4x^3)/3-x+C