Question

∫根号x乘以（1+x）分之一乘以dx

Answer 1

∫ √x/(1+x) dx
let
y =√x
dy = [1/(2√x)]dx
dx = 2ydy
∫ √x/(1+x) dx
= ∫ 2y^2/(1+y^2) dy
= 2∫ dy - 2∫ dy/(1+y^2)
=2y -2arctany + C
=2√x -2arctan√x + C