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

\int_{0}^{1} t 4 + 9 t^{2} d t

\int e^{-}

\frac{d}{d x} (\frac{1}{2 π} e^{\frac{- x ^{2}}{2}})

x \to 3 lim (\frac{x - 3}{x + 3})

x y^{^{'}} + 4 y = - 3 x

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