What is the integral of 1/((x+9)^8) ?

The integral of 1/((x+9)^8) is -1/(7(x+9)^7)+C

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

integral of 1/((x+9)^8)

\int \frac{1}{( x + 9 ) ^{8}} d x

- \frac{1}{7 ( x + 9 ) ^{7}} + C

Solution steps

\int \frac{1}{( x + 9 ) ^{8}} d x

Apply u-substitution

= \int \frac{1}{u ^{8}} d u

Apply the Power Rule

= - \frac{1}{7 u ^{7}}

Substitute back

u = x + 9

= - \frac{1}{7 ( x + 9 ) ^{7}}

Add a constant to the solution

= - \frac{1}{7 ( x + 9 ) ^{7}} + C

What is the integral of 1/((x+9)^8) ?
The integral of 1/((x+9)^8) is -1/(7(x+9)^7)+C