∫1/(1+2根号x)dx
问题描述：
∫1/(1+2根号x)dx
答
令 t = √x
∫1/(1+2√x)dx = ∫1/(1+2t)dt^2 = ∫ 2t/(1+2t)dt = ∫ 1- 1/(1+2t)dt = ∫ dt - ∫1/(1+2t)dt
= t + 1/2 ln(1+2t) + C
= √x + 1/2 ln(1+2√x) + C