What is the integral of (x-2)^{-2} ?

The integral of (x-2)^{-2} is -1/(x-2)+C

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

integral of (x-2)^{-2}

\int (x - 2)^{- 2} d x

- \frac{1}{x - 2} + C

Solution steps

\int (x - 2)^{- 2} d x

Apply exponent rule:

a^{- b} = \frac{1}{a ^{b}}

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

Apply u-substitution

: \int \frac{1}{u ^{2}} d u

= \int \frac{1}{u ^{2}} d u

Apply the Power Rule

: - \frac{1}{u}

= - \frac{1}{u}

Substitute back

u = x - 2

= - \frac{1}{x - 2}

Add a constant to the solution

= - \frac{1}{x - 2} + C

y^{^{''}} + y = 1

f (x) = sin (x)

\int 81 e^{- 9 x} sin (9 x) d x

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