What is the integral of (x-2)(x+3) ?

The integral of (x-2)(x+3) is (x^3)/3+(x^2)/2-6x+C

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integral of (x-2)(x+3)

\int (x - 2) (x + 3) d x

\frac{x ^{3}}{3} + \frac{x ^{2}}{2} - 6 x + C

Solution steps

\int (x - 2) (x + 3) d x

Expand

(x - 2) (x + 3) : x^{2} + x - 6

= \int x^{2} + x - 6 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 x d x - \int 6 d x

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

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

\int 6 d x = 6 x

= \frac{x ^{3}}{3} + \frac{x ^{2}}{2} - 6 x

Add a constant to the solution

= \frac{x ^{3}}{3} + \frac{x ^{2}}{2} - 6 x + C

f (x) = x^{\frac{1}{10}}

x \to 0 lim ((1 - 4 x)^{\frac{5}{x}})

(\frac{x}{2 - x})^{3}

(x y - x^{2} - 1) d x + (x^{2} + 1) d y = c

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

What is the integral of (x-2)(x+3) ?
The integral of (x-2)(x+3) is (x^3)/3+(x^2)/2-6x+C