If \(\frac{x^{4}+1}{x\left(x^{2}+1\right)^{2}}dx=A \log \left|x\right| +\frac{B}{1+x^{2}}+C\), then

\(A=1,B=-1\) \(A=-1,B=1\) \(A=1,B=1\) \(A=-1,B=-1\)

\(A=1,B=1\)

$\int\frac{x^{4}+1}{x\left(x^{2}+1\right)^{2}}dx=\int\frac{x^4+2x^2+1}{x(x^2+1)^2}-\frac{2x^2}{x(x^2+1)^2}dx$ $=\int\frac{1}{x}-\frac{2x}{(x^2+1)^2}dx$ $=\log x+\frac{1}{1+x^2}+C$ A = 1, B = 1