en

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular Calculus >

integral of x^2(1-x)

Solution

\int x^{2} (1 - x) d x

Solution

\frac{x ^{3}}{3} - \frac{x ^{4}}{4} + C

Solution steps

\int x^{2} (1 - x) d x

Expand

x^{2} (1 - x) : x^{2} - x^{3}

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

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

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

= \frac{x ^{3}}{3} - \frac{x ^{4}}{4}

Add a constant to the solution

= \frac{x ^{3}}{3} - \frac{x ^{4}}{4} + C

Graph

Popular Examples

integral of (sin(x))/(sqrt(x))

integral from 0 to 1 of 1/((2x-3)^2)

derivative of (192/(x^4))

derivative of sin^2(cos(4x))

(dy)/(dx)=sqrt(13x+y)-13

Frequently Asked Questions (FAQ)

What is the integral of x^2(1-x) ?
The integral of x^2(1-x) is (x^3)/3-(x^4)/4+C