计算下列反常积分:
∫+∞1arctanx/x2dx
【正确答案】:∫+∞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
- 2024-11-07 09:13:24
- 高等数学(经管类)(13125)