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Popular Calculus >

integral of 2-x^2+x

Solution

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

Solution

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

Solution steps

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

\int 2 d x = 2 x

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

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

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

Add a constant to the solution

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

Graph

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Frequently Asked Questions (FAQ)

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