(x^4+1)/(x^2(x^2+1)=A/x^2+(Bx^2+C)/(x^2+1)Ax^2+A+Bx^4+Cx^2=x^4+1B=1,A+C=0,A=1所以C=-1f(x)=(x^4+1)/(x^2(x^2+1))=1/x^2+(x^2-1)/(x^2+1)∫f(x)dx=-1/x+∫[1-2/(x^2+1)]dx=-1/x+x-2arctanx
