What is the integral of (3-4x)^5 ?

The integral of (3-4x)^5 is -1/24 (3-4x)^6+C

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

integral of (3-4x)^5

\int (3 - 4 x)^{5} d x

- \frac{1}{24} (3 - 4 x)^{6} + C

Solution steps

\int (3 - 4 x)^{5} d x

Apply u-substitution

= \int - \frac{u ^{5}}{4} d u

Take the constant out:

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

= - \frac{1}{4} \cdot \int u^{5} d u

Apply the Power Rule

= - \frac{1}{4} \cdot \frac{u ^{6}}{6}

Substitute back

u = 3 - 4 x

= - \frac{1}{4} \cdot \frac{( 3 - 4 x ) ^{6}}{6}

Simplify

- \frac{1}{4} \cdot \frac{( 3 - 4 x ) ^{6}}{6} : - \frac{1}{24} (3 - 4 x)^{6}

= - \frac{1}{24} (3 - 4 x)^{6}

Add a constant to the solution

= - \frac{1}{24} (3 - 4 x)^{6} + C