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

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

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

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

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

Solution steps

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

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

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

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

\int 2 d x = 2 x

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

Add a constant to the solution

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

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