en

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

integral of x(1-2x)

Solution

\int x (1 - 2 x) d x

Solution

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

Solution steps

\int x (1 - 2 x) d x

Expand

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

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

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

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

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

Add a constant to the solution

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

Popular Examples

derivative of (3x^2+2sqrt(x)/x)

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

derivative of cot(xcsc(x))

\frac{d}{d x} (cot (x) csc (x))

derivative of g(x)=e^{x^2-x}derivative of

g (x) = e^{x^{2} - x}

derivative of-2x+6

\frac{d}{d x} (- 2 x + 6)

integral of 8/(xln(5x))

\int \frac{8}{x ln ( 5 x )} d x

Frequently Asked Questions (FAQ)

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