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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