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

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

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

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

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

Solution steps

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

Expand

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

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

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

\int 1 d x = x

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

Add a constant to the solution

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

\int x^{3} (2 x^{4} + 4)^{2} d x

\int \frac{arctan ( x )}{x ^{2} + 1} d x

e^{x}, 2

\int \frac{a x + b}{c x + d} d x

\frac{d}{d x} (\frac{4 x ^{\frac{3}{2}}}{x})