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

The integral of x-((x^2)/2) is (x^2)/2-(x^3)/6+C

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integral of x-((x^2)/2)

integral

x - (\frac{x ^{2}}{2})

\frac{x ^{2}}{2} - \frac{x ^{3}}{6} + C

Solution steps

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

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

\int \frac{x ^{2}}{2} d x = \frac{x ^{3}}{6}

= \frac{x ^{2}}{2} - \frac{x ^{3}}{6}

Add a constant to the solution

= \frac{x ^{2}}{2} - \frac{x ^{3}}{6} + C

What is the integral of x-((x^2)/2) ?
The integral of x-((x^2)/2) is (x^2)/2-(x^3)/6+C