What is the integral of (1-2x)^9 ?

The integral of (1-2x)^9 is -1/20 (1-2x)^{10}+C

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

integral of (1-2x)^9

\int (1 - 2 x)^{9} d x

- \frac{1}{20} (1 - 2 x)^{10} + C

Solution steps

\int (1 - 2 x)^{9} d x

Apply u-substitution

= \int - \frac{u ^{9}}{2} d u

Take the constant out:

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

= - \frac{1}{2} \cdot \int u^{9} d u

Apply the Power Rule

= - \frac{1}{2} \cdot \frac{u ^{10}}{10}

Substitute back

u = 1 - 2 x

= - \frac{1}{2} \cdot \frac{( 1 - 2 x ) ^{10}}{10}

Simplify

- \frac{1}{2} \cdot \frac{( 1 - 2 x ) ^{10}}{10} : - \frac{1}{20} (1 - 2 x)^{10}

= - \frac{1}{20} (1 - 2 x)^{10}

Add a constant to the solution

= - \frac{1}{20} (1 - 2 x)^{10} + C

What is the integral of (1-2x)^9 ?
The integral of (1-2x)^9 is -1/20 (1-2x)^{10}+C