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

The integral of (ln(x+1))/((x+1)^3) is -(ln(x+1))/(2(x+1)^2)-1/(4(x+1)^2)+C

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integral of (ln(x+1))/((x+1)^3)

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

- \frac{ln ( x + 1 )}{2 ( x + 1 ) ^{2}} - \frac{1}{4 ( x + 1 ) ^{2}} + C

Solution steps

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

Apply Integration By Parts

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

\int - \frac{1}{2 ( x + 1 ) ^{3}} d x = \frac{1}{4 ( x + 1 ) ^{2}}

= - \frac{ln ( x + 1 )}{2 ( x + 1 ) ^{2}} - \frac{1}{4 ( x + 1 ) ^{2}}

Add a constant to the solution

= - \frac{ln ( x + 1 )}{2 ( x + 1 ) ^{2}} - \frac{1}{4 ( x + 1 ) ^{2}} + C

What is the integral of (ln(x+1))/((x+1)^3) ?
The integral of (ln(x+1))/((x+1)^3) is -(ln(x+1))/(2(x+1)^2)-1/(4(x+1)^2)+C