求不定积分∫1⼀(1+√x)dx

2025-02-27 16:45:12
推荐回答(1个)
回答1:

令√x = u,dx = 2u du
∫ dx/(1 + √x)
= ∫ (2u du)/(1 + u)
= 2∫ [(1 + u) - 1]/(1 + u)
= 2∫ [1 - 1/(1 + u)] du
= 2u - 2ln| 1 + u | + C