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

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

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integral of 2-(x^2)/2

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

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

Solution steps

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

\int 2 d x = 2 x

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

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

Add a constant to the solution

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