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Popular >

integral of-x+2-x^2

Solution

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

Solution

- \frac{x ^{2}}{2} + 2 x - \frac{x ^{3}}{3} + 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 d x + \int 2 d x - \int x^{2} d x

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

\int 2 d x = 2 x

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

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

Add a constant to the solution

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

Popular Examples

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\int y e^{x - y} d y

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\int 7 cos (x) + 3 sin (x) d x

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\int \frac{1}{x ( x ^{6} + 2 )} d x

integral of (2-2x)^7

\int (2 - 2 x)^{7} d x

Frequently Asked Questions (FAQ)

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