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

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

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

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

- \frac{x + 2}{x + 1} + ln ∣ x + 1 ∣ + C

Solution steps

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

Apply Integration By Parts

: - \frac{x + 2}{x + 1} - \int - \frac{1}{x + 1} d x

= - \frac{x + 2}{x + 1} - \int - \frac{1}{x + 1} d x

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

= - \frac{x + 2}{x + 1} - (- ln ∣ x + 1 ∣)

Simplify

= - \frac{x + 2}{x + 1} + ln ∣ x + 1 ∣

Add a constant to the solution

= - \frac{x + 2}{x + 1} + ln ∣ x + 1 ∣ + C

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