What is the integral of (-2)/((x-1)^3) ?

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

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integral of (-2)/((x-1)^3)

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

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

Solution steps

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

Take the constant out:

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

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

Apply u-substitution

: \int \frac{1}{u ^{3}} d u

= - 2 \cdot \int \frac{1}{u ^{3}} d u

Apply the Power Rule

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

= - 2 (- \frac{1}{2 u ^{2}})

Substitute back

u = x - 1

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

Simplify

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

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

Add a constant to the solution

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

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