计算下列反常积分： ∫+∞01/(x2+2x+2)dx

计算下列反常积分：
∫+∞01/(x2+2x+2)dx
【正确答案】：∫+∞01/(x2+2x+2)dx =∫+∞01/[1+(x+1)2]d(x+1) =arctan(x+1)|+∞0． =π/2-π/4 =π/4