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

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

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

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

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

Solution steps

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

Apply u-substitution

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

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

Take the constant out:

\int a \cdot f (x) d x = a \cdot \int f (x) d x

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

Apply the Power Rule

: - \frac{1}{u}

= - (- \frac{1}{u})

Substitute back

u = 1 - x

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

Simplify

= \frac{1}{1 - x}

Add a constant to the solution

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

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