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

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

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

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

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

Solution steps

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

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

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

\int c d x = c x

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

Add a constant to the solution

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

n = 1 \sum \infty \frac{1}{n ^{2} + 6 n + 8}

x \to 0 lim (\frac{( cos ( x ) )}{x})

\frac{d}{d x} (\frac{1}{1 + 4 x ^{2}})

\frac{d}{d t} (π t)

x \to 0 lim (\frac{( sin ( 8 x ) )}{x})

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