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

= - \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

y^{^{'}} = (x + 1) \cdot (y + 1)

x \to π lim (tan (\frac{5}{6} x))

(x^{2} - 1) \frac{d y}{d x} = x (y - 1)

\frac{d}{d x} (7 x^{2} + 1)

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

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