What is the integral of (-2x^2+6x) ?

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

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integral of (-2x^2+6x)

\int (- 2 x^{2} + 6 x) d x

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

Solution steps

\int - 2 x^{2} + 6 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 2 x^{2} d x + \int 6 x d x

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

\int 6 x d x = 3 x^{2}

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

Add a constant to the solution

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

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