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

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

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integral of (-x^2+2x)

\int (- x^{2} + 2 x) d x

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

Solution steps

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

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

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

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

Add a constant to the solution

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

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