What is the integral of (1/(x-1))^7 ?

The integral of (1/(x-1))^7 is -1/(6(x-1)^6)+C

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integral of (1/(x-1))^7

\int (\frac{1}{x - 1})^{7} d x

- \frac{1}{6 ( x - 1 ) ^{6}} + C

Solution steps

\int (\frac{1}{x - 1})^{7} d x

Simplify

(\frac{1}{x - 1})^{7} : \frac{1}{( x - 1 ) ^{7}}

= \int \frac{1}{( x - 1 ) ^{7}} d x

Apply u-substitution

: \int \frac{1}{u ^{7}} d u

= \int \frac{1}{u ^{7}} d u

Apply the Power Rule

: - \frac{1}{6 u ^{6}}

= - \frac{1}{6 u ^{6}}

Substitute back

u = x - 1

= - \frac{1}{6 ( x - 1 ) ^{6}}

Add a constant to the solution

= - \frac{1}{6 ( x - 1 ) ^{6}} + C

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What is the integral of (1/(x-1))^7 ?
The integral of (1/(x-1))^7 is -1/(6(x-1)^6)+C