What is the integral of 1/((x-3)^5) ?

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

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

integral of 1/((x-3)^5)

\int \frac{1}{( x - 3 ) ^{5}} d x

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

Solution steps

\int \frac{1}{( x - 3 ) ^{5}} d x

Apply u-substitution

= \int \frac{1}{u ^{5}} d u

Apply the Power Rule

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

Substitute back

u = x - 3

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

Add a constant to the solution

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

What is the integral of 1/((x-3)^5) ?
The integral of 1/((x-3)^5) is -1/(4(x-3)^4)+C