What is the integral of x(x-2021) ?

The integral of x(x-2021) is (x^3)/3-(2021x^2)/2+C

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integral of x(x-2021)

\int x (x - 2021) d x

\frac{x ^{3}}{3} - \frac{2021 x ^{2}}{2} + C

Solution steps

\int x (x - 2021) d x

Expand

x (x - 2021) : x^{2} - 2021 x

= \int x^{2} - 2021 x 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 2021 x d x

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

\int 2021 x d x = \frac{2021 x ^{2}}{2}

= \frac{x ^{3}}{3} - \frac{2021 x ^{2}}{2}

Add a constant to the solution

= \frac{x ^{3}}{3} - \frac{2021 x ^{2}}{2} + C

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What is the integral of x(x-2021) ?
The integral of x(x-2021) is (x^3)/3-(2021x^2)/2+C