What is the integral of (x+7)(x-3) ?

The integral of (x+7)(x-3) is (x^3)/3+2x^2-21x+C

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integral of (x+7)(x-3)

\int (x + 7) (x - 3) d x

\frac{x ^{3}}{3} + 2 x^{2} - 21 x + C

Solution steps

\int (x + 7) (x - 3) d x

Expand

(x + 7) (x - 3) : x^{2} + 4 x - 21

= \int x^{2} + 4 x - 21 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 4 x d x - \int 21 d x

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

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

\int 21 d x = 21 x

= \frac{x ^{3}}{3} + 2 x^{2} - 21 x

Add a constant to the solution

= \frac{x ^{3}}{3} + 2 x^{2} - 21 x + C

\int 4 x - 4 d x

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

2 (x - 1)

\int e^{2 y - y^{2}} d y

x \to 3 lim (x - x)

What is the integral of (x+7)(x-3) ?
The integral of (x+7)(x-3) is (x^3)/3+2x^2-21x+C