What is the integral of (x-1)(x+2)(x-3) ?

The integral of (x-1)(x+2)(x-3) is (x^4)/4-(2x^3)/3-(5x^2)/2+6x+C

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integral of (x-1)(x+2)(x-3)

\int (x - 1) (x + 2) (x - 3) d x

\frac{x ^{4}}{4} - \frac{2 x ^{3}}{3} - \frac{5 x ^{2}}{2} + 6 x + C

Solution steps

\int (x - 1) (x + 2) (x - 3) d x

Expand

(x - 1) (x + 2) (x - 3) : x^{3} - 2 x^{2} - 5 x + 6

= \int x^{3} - 2 x^{2} - 5 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^{3} d x - \int 2 x^{2} d x - \int 5 x d x + \int 6 d x

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

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

\int 5 x d x = \frac{5 x ^{2}}{2}

\int 6 d x = 6 x

= \frac{x ^{4}}{4} - \frac{2 x ^{3}}{3} - \frac{5 x ^{2}}{2} + 6 x

Add a constant to the solution

= \frac{x ^{4}}{4} - \frac{2 x ^{3}}{3} - \frac{5 x ^{2}}{2} + 6 x + C

f (x) = \frac{4 x}{x ^{3} + 5}

\int \frac{80}{64 - x ^{2}} d x

\frac{\partial}{\partial x} (f (x, b, y) (a x + b y))

5 x, \frac{1}{7} x, 50 - x^{2}

(x^{2} + 1) y^{^{'}} + 7 x (y - 1) = 0, y (0) = 4

What is the integral of (x-1)(x+2)(x-3) ?
The integral of (x-1)(x+2)(x-3) is (x^4)/4-(2x^3)/3-(5x^2)/2+6x+C