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

The integral of (2x-3)(x-3) is (2x^3)/3-(9x^2)/2+9x+C

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

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

\frac{2 x ^{3}}{3} - \frac{9 x ^{2}}{2} + 9 x + C

Solution steps

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

Expand

(2 x - 3) (x - 3) : 2 x^{2} - 9 x + 9

= \int 2 x^{2} - 9 x + 9 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 2 x^{2} d x - \int 9 x d x + \int 9 d x

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

\int 9 x d x = \frac{9 x ^{2}}{2}

\int 9 d x = 9 x

= \frac{2 x ^{3}}{3} - \frac{9 x ^{2}}{2} + 9 x

Add a constant to the solution

= \frac{2 x ^{3}}{3} - \frac{9 x ^{2}}{2} + 9 x + C

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What is the integral of (2x-3)(x-3) ?
The integral of (2x-3)(x-3) is (2x^3)/3-(9x^2)/2+9x+C