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

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

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

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

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

Solution steps

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

Simplify

= \int - x^{2} - 3 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 x^{2} d x - \int 3 x d x + \int 4 d x

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

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

\int 4 d x = 4 x

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

Add a constant to the solution

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

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