What is the integral of (x(x-1))/2 ?

The integral of (x(x-1))/2 is 1/2 ((x^3)/3-(x^2)/2)+C

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integral of (x(x-1))/2

\int \frac{x ( x - 1 )}{2} d x

\frac{1}{2} (\frac{x ^{3}}{3} - \frac{x ^{2}}{2}) + C

Solution steps

\int \frac{x ( x - 1 )}{2} d x

Take the constant out:

\int a \cdot f (x) d x = a \cdot \int f (x) d x

= \frac{1}{2} \cdot \int x (x - 1) d x

Expand

x (x - 1) : x^{2} - x

= \frac{1}{2} \cdot \int x^{2} - x 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

= \frac{1}{2} (\int x^{2} d x - \int x d x)

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

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

= \frac{1}{2} (\frac{x ^{3}}{3} - \frac{x ^{2}}{2})

Add a constant to the solution

= \frac{1}{2} (\frac{x ^{3}}{3} - \frac{x ^{2}}{2}) + C

x \to 0 lim (1 + sin^{2} (3 x))

\frac{d ^{2}}{d x ^{2}} (sin (x) cos (x))

\int (\frac{( x - 3 )}{( x + 2 )}) d x

\frac{\partial}{\partial x} (9)

y^{^{'}} = a^{x + y}

What is the integral of (x(x-1))/2 ?
The integral of (x(x-1))/2 is 1/2 ((x^3)/3-(x^2)/2)+C