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

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

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

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

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

Solution steps

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

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

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

\int 2 d x = 2 x

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

Add a constant to the solution

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

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