求下列不定积分：∫[(1+2x2)/x2(1+x2)]dx．
∫=(1+2x2)/x2(1+x2)=∫[(1+x2)+x2]/[x2(1+x2)]dx=∫{1/x2+[1/(1+x22)]}dx=-(1/x)arctanx+c．
求下列不定积分：∫[(1+2x2)/x2(1+x2)]dx．
∫=(1+2x2)/x2(1+x2)=∫[(1+x2)+x2]/[x2(1+x2)]dx=∫{1/x2+[1/(1+x22)]}dx=-(1/x)arctanx+c．
