en

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

integral of x(x^2-2)

Solution

\int x (x^{2} - 2) d x

Solution

\frac{x ^{4}}{4} - x^{2} + C

Solution steps

\int x (x^{2} - 2) d x

Expand

x (x^{2} - 2) : x^{3} - 2 x

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

\int x^{3} d x = \frac{x ^{4}}{4}

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

= \frac{x ^{4}}{4} - x^{2}

Add a constant to the solution

= \frac{x ^{4}}{4} - x^{2} + C

Popular Examples

(f(t)\circ g(t))'

(f (t) \circ g (t))^{'}

integral from 2 to 3 of (x+1)/(x^2-x)

\int_{2}^{3} \frac{x + 1}{x ^{2} - x} d x

limit as x approaches 1 of (3x+2)/(4x-5)

x \to 1 lim (\frac{3 x + 2}{4 x - 5})

(\partial)/(\partial x)(10-(3x^2+3y^2))

\frac{\partial}{\partial x} (10 - (3 x^{2} + 3 y^{2}))

derivative of 3x^2-4x+1

\frac{d}{d x} (3 x^{2} - 4 x + 1)

Frequently Asked Questions (FAQ)

What is the integral of x(x^2-2) ?
The integral of x(x^2-2) is (x^4)/4-x^2+C