What is the integral of-x^3+x^2+2x ?

The integral of-x^3+x^2+2x is -(x^4)/4+(x^3)/3+x^2+C

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integral of-x^3+x^2+2x

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

- \frac{x ^{4}}{4} + \frac{x ^{3}}{3} + x^{2} + C

Solution steps

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

\int x^{3} d x = \frac{x ^{4}}{4}

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

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

= - \frac{x ^{4}}{4} + \frac{x ^{3}}{3} + x^{2}

Add a constant to the solution

= - \frac{x ^{4}}{4} + \frac{x ^{3}}{3} + x^{2} + C

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What is the integral of-x^3+x^2+2x ?
The integral of-x^3+x^2+2x is -(x^4)/4+(x^3)/3+x^2+C