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Popular >

integral of x(x-1)

Solution

\int x (x - 1) d x

Solution

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

Solution steps

\int x (x - 1) d x

Expand

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

= \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

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

Add a constant to the solution

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

Popular Examples

(d^2)/(dx^2)((x^2+6)^7)

\frac{d ^{2}}{d x ^{2}} ((x^{2} + 6)^{7})

area g(x)=sin(x),0, pi/4 area

g (x) = sin (x), 0, \frac{π}{4}

derivative of (x^2+1(x^2-1))

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

sum from n=2 to infinity of n/(2^{n-1)}

n = 2 \sum \infty \frac{n}{2 ^{n - 1}}

inverse oflaplace 5/((s^2+2s+2))inverse laplace

\frac{5}{( s ^{2} + 2 s + 2 )}

Frequently Asked Questions (FAQ)

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