What is the integral of 1/((x-5)^2) ?

The integral of 1/((x-5)^2) is -1/(x-5)+C

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integral of 1/((x-5)^2)

\int \frac{1}{( x - 5 ) ^{2}} d x

- \frac{1}{x - 5} + C

Solution steps

\int \frac{1}{( x - 5 ) ^{2}} d x

Apply u-substitution

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

Apply the Power Rule

= - \frac{1}{u}

Substitute back

u = x - 5

= - \frac{1}{x - 5}

Add a constant to the solution

= - \frac{1}{x - 5} + C