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^2-4)

Solution

\int x (x^{2} - 4) d x

Solution

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

Solution steps

\int x (x^{2} - 4) d x

Expand

x (x^{2} - 4) : x^{3} - 4 x

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

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

\int 4 x d x = 2 x^{2}

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

Add a constant to the solution

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

Popular Examples

sum from n=1 to infinity of 2/(nln(7n))

n = 1 \sum \infty \frac{2}{n ln ( 7 n )}

integral of sin(x/3)

\int sin (\frac{x}{3}) d x

integral of e^{x/2}sin(3x)

\int e^{\frac{x}{2}} sin (3 x) d x

integral of \sqrt[7]{x^6}

(\partial)/(\partial y)(3x-2y^4)

\frac{\partial}{\partial y} (3 x - 2 y^{4})

Frequently Asked Questions (FAQ)

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