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

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

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

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

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

Solution steps

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

Apply Integration By Parts

= - \frac{x + 1}{x - 5} - \int - \frac{1}{x - 5} d x

\int - \frac{1}{x - 5} d x = - ln ∣ x - 5 ∣

= - \frac{x + 1}{x - 5} - (- ln ∣ x - 5 ∣)

Simplify

= - \frac{x + 1}{x - 5} + ln ∣ x - 5 ∣

Add a constant to the solution

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

What is the integral of (x+1)/((x-5)^2) ?
The integral of (x+1)/((x-5)^2) is -(x+1)/(x-5)+ln|x-5|+C