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

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

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

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

- \frac{x + 1}{x - 3} + ln ∣ x - 3 ∣ + C

Solution steps

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

Apply Integration By Parts

= - \frac{x + 1}{x - 3} - \int - \frac{1}{x - 3} d x

\int - \frac{1}{x - 3} d x = - ln ∣ x - 3 ∣

= - \frac{x + 1}{x - 3} - (- ln ∣ x - 3 ∣)

Simplify

= - \frac{x + 1}{x - 3} + ln ∣ x - 3 ∣

Add a constant to the solution

= - \frac{x + 1}{x - 3} + ln ∣ x - 3 ∣ + C

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