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

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

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integral of (x^2)/2+c

\int \frac{x ^{2}}{2} + c d x

\frac{x ^{3}}{6} + c x + C

Solution steps

\int \frac{x ^{2}}{2} + c 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 \frac{x ^{2}}{2} d x + \int c d x

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

\int c d x = c x

= \frac{x ^{3}}{6} + c x

Add a constant to the solution

= \frac{x ^{3}}{6} + c x + C

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