计算反常积分：∫+∞1xe-x2dx

计算反常积分：
∫+∞1xe-x2dx
【正确答案】：解：∫+∞1xe-x2dx =-1/2∫+∞1e-x2d(-x2) =-1/2e-x2|+1 =-1/2×(0-e-1) =1/2e