What is the integral of (1-x)^5 ?

The integral of (1-x)^5 is -((1-x)^6)/6+C

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

integral of (1-x)^5

integral

(1 - x)^{5}

- \frac{( 1 - x ) ^{6}}{6} + C

Solution steps

\int (1 - x)^{5} d x

Apply u-substitution

: \int - u^{5} d u

= \int - u^{5} d u

Take the constant out:

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

= - \int u^{5} d u

Apply the Power Rule

: \frac{u ^{6}}{6}

= - \frac{u ^{6}}{6}

Substitute back

u = 1 - x

= - \frac{( 1 - x ) ^{6}}{6}

Add a constant to the solution

= - \frac{( 1 - x ) ^{6}}{6} + C

\frac{- 1}{( 1 + x ^{2} )}

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

x^{2} x + 2

\frac{1 + 1}{x ^{4}}

\frac{e ^{x} + 1}{e ^{x}}