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

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

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

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

\frac{x ^{4}}{4} - \frac{x ^{2}}{2} + \frac{2 x ^{3}}{3} - 2 x + C

Solution steps

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

Expand

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

= \int x^{3} - x + 2 x^{2} - 2 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 x d x + \int 2 x^{2} d x - \int 2 d x

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

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

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

\int 2 d x = 2 x

= \frac{x ^{4}}{4} - \frac{x ^{2}}{2} + \frac{2 x ^{3}}{3} - 2 x

Add a constant to the solution

= \frac{x ^{4}}{4} - \frac{x ^{2}}{2} + \frac{2 x ^{3}}{3} - 2 x + C

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