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

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

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

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

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

Solution steps

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

Expand

(x - 3) (x - 1) : x^{2} - 4 x + 3

= \int x^{2} - 4 x + 3 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 3 d x

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

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

\int 3 d x = 3 x

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

Add a constant to the solution

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

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