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

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

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integral of 1/((u-1)^3)

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

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

Solution steps

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

Apply u-substitution

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

= \int \frac{1}{v ^{3}} d v

Apply the Power Rule

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

= - \frac{1}{2 v ^{2}}

Substitute back

v = u - 1

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

Add a constant to the solution

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

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