en

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

integral of (-x)/3

Solution

\int \frac{- x}{3} d x

Solution

- \frac{x ^{2}}{6} + C

Solution steps

\int \frac{- x}{3} d x

Take the constant out:

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

= \frac{- 1}{3} \cdot \int x d x

Simplify

= (- \frac{1}{3}) \cdot \int x d x

Apply the Power Rule

: \frac{x ^{2}}{2}

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

Simplify

(- \frac{1}{3}) \frac{x ^{2}}{2} : - \frac{x ^{2}}{6}

= - \frac{x ^{2}}{6}

Add a constant to the solution

= - \frac{x ^{2}}{6} + C

Graph

Popular Examples

integral from 6 to x of 1/20+x/(40)

\int_{6}^{x} \frac{1}{20} + \frac{x}{40} d x

(\partial)/(\partial x)(3/(x^2))

\frac{\partial}{\partial x} (\frac{3}{x ^{2}})

integral of sin^8(x)cos(x)

\int sin^{8} (x) cos (x) d x

(\partial)/(\partial x)(2arctan(x))

\frac{\partial}{\partial x} (2 arctan (x))

integral of (x^2+8x-3)/(x^3+3x^2)

\int \frac{x ^{2} + 8 x - 3}{x ^{3} + 3 x ^{2}} d x

Frequently Asked Questions (FAQ)

What is the integral of (-x)/3 ?
The integral of (-x)/3 is -(x^2)/6+C