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

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

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

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

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

Solution steps

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

\int 2 d x = 2 x

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

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

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

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

Add a constant to the solution

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

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