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$\int \frac{d x}{x\left(x^{2}+1\right)}$ equals

• A
  $\log |x|-\frac{1}{2} \log \left(x^{2}+1\right)+C$
• B
  $\log | x |+\frac{1}{2} \log \left(x^{2}+1\right)+C$
• C
  $-\log |x|+\frac{1}{2} \log \left(x^{2}+1\right)+C$
• D
  $\frac{1}{2} \log |x|+\log \left(x^{2}+1\right)+C$