What is the integral of-2x^2+2x+4 ?

The integral of-2x^2+2x+4 is -(2x^3)/3+x^2+4x+C

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integral of-2x^2+2x+4

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

- \frac{2 x ^{3}}{3} + x^{2} + 4 x + C

Solution steps

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

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

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

\int 4 d x = 4 x

= - \frac{2 x ^{3}}{3} + x^{2} + 4 x

Add a constant to the solution

= - \frac{2 x ^{3}}{3} + x^{2} + 4 x + C

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What is the integral of-2x^2+2x+4 ?
The integral of-2x^2+2x+4 is -(2x^3)/3+x^2+4x+C