Question

（x的平方加1）分之（e的x次方乘x ）的不定积分

如图 要过程哦

Answer 1

∫ 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

追问

明显不是我的题