$\int \frac{\log x}{(1+x)^3} d x=$

• A

  $\frac{1}{2}\left[\frac{1}{1+x}+\frac{\log x}{(1+x)^2}-\log \left(x^2+x\right)\right]+\mathrm{c}$
• B

  $\frac{1}{2}\left[\frac{1}{1+x}-\frac{\log x}{(1+x)}-\log \left(1+x^2\right)\right]+\mathrm{c}$
• C

  $\frac{1}{2}\left[\frac{1}{1+x}+\frac{\log x}{(1+x)^2}-\log \left(1+x^2\right)\right]+\mathrm{c}$
• Correct answer
  D

  $\frac{1}{2}\left[\frac{1}{1+x}-\frac{\log x}{(1+x)^2}+\log \left(\frac{x}{1+x}\right)\right]+\mathrm{c}$

Hence, the correct answer is option: 'D'.