en

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular Calculus >

integral of (1-x)^3

Solution

\int (1 - x)^{3} d x

Solution

x - \frac{3 x ^{2}}{2} + x^{3} - \frac{x ^{4}}{4} + C

Solution steps

\int (1 - x)^{3} d x

Expand

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

= \int 1 - 3 x + 3 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 1 d x - \int 3 x d x + \int 3 x^{2} d x - \int x^{3} d x

\int 1 d x = x

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

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

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

= x - \frac{3 x ^{2}}{2} + x^{3} - \frac{x ^{4}}{4}

Add a constant to the solution

= x - \frac{3 x ^{2}}{2} + x^{3} - \frac{x ^{4}}{4} + C

Graph

Popular Examples

integral from 0 to 1 of (4sqrt(x))-(4x)

derivative of (pix/2)

integral of sqrt(12-x^2)

7x-4ysqrt(x^2+1)(dy)/(dx)=0

integral of x/((x-1))

Frequently Asked Questions (FAQ)

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