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Popular Calculus >

integral of 2+x-x^2

Solution

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

Solution

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

Solution steps

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

\int 2 d x = 2 x

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

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

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

Add a constant to the solution

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

Graph

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Frequently Asked Questions (FAQ)

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