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Popular >

integral of-x^2+x+2

Solution

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

Solution

- \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

Graph

Popular Examples

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\int (8 x - 5^{x}) d x

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x \to 0 lim (1 - \frac{2}{3 x})

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x \to π lim (\frac{cos ( x ) - 1}{x})

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\frac{d}{d x} (x (x - 9)^{2})

Frequently Asked Questions (FAQ)

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