作业帮(x乘以e的x次幂)/(x+1)的平方的不定积分
来源：学生作业帮 编辑：作业帮 分类：数学作业 时间：2024/05/15 01:02:13
(x乘以e的x次幂)/(x+1)的平方的不定积分
∫ xe^x/(x + 1)² dx
= ∫ [(x + 1) - 1]e^x/(x + 1)² dx
= ∫ e^x/(x + 1) dx - ∫ e^x/(x + 1)² dx
= ∫ e^x/(x + 1) dx - ∫ e^x d[- 1/(x + 1)]
= ∫ e^x/(x + 1) dx + e^x/(x + 1) - ∫ 1/(x + 1) d(e^x),分部积分法
= ∫ e^x/(x + 1) dx + e^x/(x + 1) - ∫ e^x/(x + 1) dx
= e^x/(x + 1) + C
= ∫ [(x + 1) - 1]e^x/(x + 1)² dx
= ∫ e^x/(x + 1) dx - ∫ e^x/(x + 1)² dx
= ∫ e^x/(x + 1) dx - ∫ e^x d[- 1/(x + 1)]
= ∫ e^x/(x + 1) dx + e^x/(x + 1) - ∫ 1/(x + 1) d(e^x),分部积分法
= ∫ e^x/(x + 1) dx + e^x/(x + 1) - ∫ e^x/(x + 1) dx
= e^x/(x + 1) + C