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

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

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

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

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

Solution steps

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

Apply Integration By Parts

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

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

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

Simplify

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

Add a constant to the solution

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

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