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

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

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integral of x^2+x-x^3

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

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

Solution steps

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

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

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

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

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

Add a constant to the solution

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

\int (3 x - 1) (3 x + 1) d x

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