What is the integral of (2x+9)^5 ?

The integral of (2x+9)^5 is 1/12 (2x+9)^6+C

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

integral of (2x+9)^5

\int (2 x + 9)^{5} d x

\frac{1}{12} (2 x + 9)^{6} + C

Solution steps

\int (2 x + 9)^{5} d x

Apply u-substitution

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

Apply the Power Rule

= \frac{1}{2} \cdot \frac{u ^{6}}{6}

Substitute back

u = 2 x + 9

= \frac{1}{2} \cdot \frac{( 2 x + 9 ) ^{6}}{6}

Simplify

\frac{1}{2} \cdot \frac{( 2 x + 9 ) ^{6}}{6} : \frac{1}{12} (2 x + 9)^{6}

= \frac{1}{12} (2 x + 9)^{6}

Add a constant to the solution

= \frac{1}{12} (2 x + 9)^{6} + C