If (x^4+1)/(x≤ft(x^2+1)^2)dx=A log ≤ft|x| +B/(1+x^2)+C , then

$\int\frac{x^{4}+1}{x\left(x^{2}+1\right)^{2}}dx=\int\frac{x^4+2x^2+1}{x(x^2+1)^2}-\frac{2x^2}{x(x^2+1)^2}dx$

$=\int\frac{1}{x}-\frac{2x}{(x^2+1)^2}dx$

$=\log x+\frac{1}{1+x^2}+C$

A = 1, B = 1