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

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

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

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

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

Solution steps

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

Apply Integration By Parts

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

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

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

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

Simplify

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

Add a constant to the solution

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

\int 3 x^{\frac{1}{2}} d x

y = x^{3} + 3 x^{2} + 2

\frac{d}{d x} \frac{e ^{- t}}{( x ^{2} + y ( t , x ) ^{2} ) ^{2}}

\int \frac{sec ^{2} ( x )}{tan ^{4} ( x )} d x

y^{^{'}} + x y = x y^{2}

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