What is the integral of (x-1)^{-2} ?

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

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integral of (x-1)^{-2}

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

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

Solution steps

\int (x - 1)^{- 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 - 1

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

Add a constant to the solution

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

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