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

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

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

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

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

Solution steps

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

Simplify

(\frac{1}{x - 1})^{2} : \frac{1}{( x - 1 ) ^{2}}

= \int \frac{1}{( 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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