计算下列反常积分：
∫+∞1arctanx/x2dx
∫+∞1arctanx/x2dx =-∫+∞1arctanxd1/x =-[arctanx/x|+∞1-∫+∞11/x•1/(1+x2)dx] =π/4+∫+∞1[1/x-x/(1+x2)]dx =π/4+lnx|+∞1-1/2∫+∞11/(1+x2)d(1+x2) =π/4+lnx|+∞1-1/2ln(1+x2)|+∞1 =π/4+ln2/2
计算下列反常积分：
∫+∞1arctanx/x2dx
∫+∞1arctanx/x2dx =-∫+∞1arctanxd1/x =-[arctanx/x|+∞1-∫+∞11/x•1/(1+x2)dx] =π/4+∫+∞1[1/x-x/(1+x2)]dx =π/4+lnx|+∞1-1/2∫+∞11/(1+x2)d(1+x2) =π/4+lnx|+∞1-1/2ln(1+x2)|+∞1 =π/4+ln2/2
