en

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

integral of x^2-x

Solution

\int x^{2} - x d x

Solution

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

Solution steps

\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

derivative of |x-4|

\frac{d}{d x} (∣ x - 4 ∣)

derivative of sin^3(x^2-1)

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

integral of (x+arctan(x))/(1+x^2)

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

derivative of x^{arcsin(x})

\frac{d}{d x} (x^{a r c s i n (x)})

derivative of (4x+4sqrt(1+x)/(x^2-1))

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

Frequently Asked Questions (FAQ)

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