What is the integral of 1/((x-2)^4) ?

The integral of 1/((x-2)^4) is -1/(3(x-2)^3)+C

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

integral of 1/((x-2)^4)

\int \frac{1}{( x - 2 ) ^{4}} d x

- \frac{1}{3 ( x - 2 ) ^{3}} + C

Solution steps

\int \frac{1}{( x - 2 ) ^{4}} d x

Apply u-substitution

: \int \frac{1}{u ^{4}} d u

= \int \frac{1}{u ^{4}} d u

Apply the Power Rule

: - \frac{1}{3 u ^{3}}

= - \frac{1}{3 u ^{3}}

Substitute back

u = x - 2

= - \frac{1}{3 ( x - 2 ) ^{3}}

Add a constant to the solution

= - \frac{1}{3 ( x - 2 ) ^{3}} + C

x \to π lim (\frac{tan ( x )}{sin ( 2 x )})

\frac{d}{d x} (x + y + z)

\frac{d}{d x} (e^{x} + e^{x})

\frac{\partial}{\partial y} (sin (x) cos (x))

9 e^{- x}

What is the integral of 1/((x-2)^4) ?
The integral of 1/((x-2)^4) is -1/(3(x-2)^3)+C